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"text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{l}\n", "\\begin{array}{lcrcrcrcrcrcrcrcrcrcrcrcrcrcrcrcrcrcrcrcrcrcrcrcrcrcl}\n", " \\min \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} 1000 x_{1} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 6 x_{2} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 7 x_{3} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 1000 x_{4} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 8 x_{5} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 6 x_{6} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 1000 x_{7} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 5 x_{8} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 4 x_{9} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 7 x_{10} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 7 x_{11} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 5 x_{12} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 1000 x_{13} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 3 x_{14} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 1000 x_{15} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 2 x_{16} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 4 x_{17} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 3 x_{18} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 1000 x_{19} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 5 x_{20} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 8 x_{21} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 7 x_{22} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 4 x_{23} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 5 x_{24} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 1000 x_{25} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\\\\n", " \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} x_{1} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} x_{2} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} x_{3} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} x_{4} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} x_{5} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} = \\mspace{-6mu}&\\mspace{-6mu} 1 \\\\\n", " \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} x_{6} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} x_{7} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} x_{8} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} x_{9} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} x_{10} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} = \\mspace{-6mu}&\\mspace{-6mu} 1 \\\\\n", " \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} x_{11} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} x_{12} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} x_{13} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} x_{14} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} x_{15} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} = \\mspace{-6mu}&\\mspace{-6mu} 1 \\\\\n", " \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} x_{16} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} x_{17} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} x_{18} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} x_{19} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} x_{20} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} = \\mspace{-6mu}&\\mspace{-6mu} 1 \\\\\n", " \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} x_{21} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} x_{22} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} x_{23} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} x_{24} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} x_{25} \\mspace{-6mu}&\\mspace{-6mu} = \\mspace{-6mu}&\\mspace{-6mu} 1 \\\\\n", " \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} x_{1} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} x_{6} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} x_{11} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} x_{16} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} x_{21} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} = \\mspace{-6mu}&\\mspace{-6mu} 1 \\\\\n", " \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} x_{2} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} x_{7} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} x_{12} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} x_{17} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} x_{22} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} = \\mspace{-6mu}&\\mspace{-6mu} 1 \\\\\n", " \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} x_{3} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} x_{8} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} x_{13} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} x_{18} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} x_{23} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} = \\mspace{-6mu}&\\mspace{-6mu} 1 \\\\\n", " \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} x_{4} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} x_{9} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} x_{14} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} x_{19} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} x_{24} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} = \\mspace{-6mu}&\\mspace{-6mu} 1 \\\\\n", " \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} x_{5} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} x_{10} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} x_{15} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} x_{20} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} x_{25} \\mspace{-6mu}&\\mspace{-6mu} = \\mspace{-6mu}&\\mspace{-6mu} 1 \\\\\n", "\\end{array} \\\\\n", "x_{1}, x_{2}, x_{3}, x_{4}, x_{5}, x_{6}, x_{7}, x_{8}, x_{9}, x_{10}, x_{11}, x_{12}, x_{13}, x_{14}, x_{15}, x_{16}, x_{17}, x_{18}, x_{19}, x_{20}, x_{21}, x_{22}, x_{23}, x_{24}, x_{25} \\geq 0\n", "\\end{array}$$" ], "text/plain": [ "LP problem (use 'view(...)' or '%display typeset' for details)" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}22$$" ], "text/plain": [ "22" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(0,\\,1,\\,0,\\,0,\\,0,\\,0,\\,0,\\,0,\\,0,\\,1,\\,0,\\,0,\\,0,\\,1,\\,0,\\,1,\\,0,\\,0,\\,0,\\,0,\\,0,\\,0,\\,1,\\,0,\\,0\\right)$$" ], "text/plain": [ "(0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0)" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$$" ], "text/plain": [ "ry" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$$" ], "text/plain": [ "ry" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{}$$" ], "text/plain": [ "salto" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{\\texttt{El dual es:}}$$" ], "text/plain": [ "dual" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$$" ], "text/plain": [ "ry" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{l}\n", "\\begin{array}{lcrcrcrcrcrcrcrcrcrcrcl}\n", " \\max \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} y_{1} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} y_{2} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} y_{3} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} y_{4} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} y_{5} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} y_{6} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} y_{7} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} y_{8} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} y_{9} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} y_{10} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\\\\n", " \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} y_{1} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} y_{6} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\leq \\mspace{-6mu}&\\mspace{-6mu} 1000 \\\\\n", " \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} y_{1} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} y_{7} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\leq \\mspace{-6mu}&\\mspace{-6mu} 6 \\\\\n", " \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} y_{1} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} y_{8} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\leq \\mspace{-6mu}&\\mspace{-6mu} 7 \\\\\n", " \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} y_{1} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} y_{9} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\leq \\mspace{-6mu}&\\mspace{-6mu} 1000 \\\\\n", " \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} y_{1} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} y_{10} \\mspace{-6mu}&\\mspace{-6mu} \\leq \\mspace{-6mu}&\\mspace{-6mu} 8 \\\\\n", " \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} y_{2} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} y_{6} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\leq \\mspace{-6mu}&\\mspace{-6mu} 6 \\\\\n", " \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} y_{2} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} y_{7} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\leq \\mspace{-6mu}&\\mspace{-6mu} 1000 \\\\\n", " \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} y_{2} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} y_{8} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\leq \\mspace{-6mu}&\\mspace{-6mu} 5 \\\\\n", " \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} y_{2} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} y_{9} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\leq \\mspace{-6mu}&\\mspace{-6mu} 4 \\\\\n", " \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} y_{2} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} y_{10} \\mspace{-6mu}&\\mspace{-6mu} \\leq \\mspace{-6mu}&\\mspace{-6mu} 7 \\\\\n", " \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} y_{3} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} y_{6} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\leq \\mspace{-6mu}&\\mspace{-6mu} 7 \\\\\n", " \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} y_{3} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} y_{7} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\leq \\mspace{-6mu}&\\mspace{-6mu} 5 \\\\\n", " \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} y_{3} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} y_{8} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\leq \\mspace{-6mu}&\\mspace{-6mu} 1000 \\\\\n", " \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} y_{3} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} y_{9} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\leq \\mspace{-6mu}&\\mspace{-6mu} 3 \\\\\n", " \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} y_{3} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} y_{10} \\mspace{-6mu}&\\mspace{-6mu} \\leq \\mspace{-6mu}&\\mspace{-6mu} 1000 \\\\\n", " \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} y_{4} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} y_{6} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\leq \\mspace{-6mu}&\\mspace{-6mu} 2 \\\\\n", " \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} y_{4} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} y_{7} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\leq \\mspace{-6mu}&\\mspace{-6mu} 4 \\\\\n", " \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} y_{4} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} y_{8} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\leq \\mspace{-6mu}&\\mspace{-6mu} 3 \\\\\n", " \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} y_{4} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} y_{9} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\leq \\mspace{-6mu}&\\mspace{-6mu} 1000 \\\\\n", " \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} y_{4} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} y_{10} \\mspace{-6mu}&\\mspace{-6mu} \\leq \\mspace{-6mu}&\\mspace{-6mu} 5 \\\\\n", " \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} y_{5} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} y_{6} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\leq \\mspace{-6mu}&\\mspace{-6mu} 8 \\\\\n", " \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} y_{5} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} y_{7} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\leq \\mspace{-6mu}&\\mspace{-6mu} 7 \\\\\n", " \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} y_{5} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} y_{8} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\leq \\mspace{-6mu}&\\mspace{-6mu} 4 \\\\\n", " \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} y_{5} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} y_{9} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\leq \\mspace{-6mu}&\\mspace{-6mu} 5 \\\\\n", " \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} y_{5} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} y_{10} \\mspace{-6mu}&\\mspace{-6mu} \\leq \\mspace{-6mu}&\\mspace{-6mu} 1000 \\\\\n", "\\end{array} \\\\\n", "\n", "\\end{array}$$" ], "text/plain": [ "LP problem (use 'view(...)' or '%display typeset' for details)" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$$" ], "text/plain": [ "ry" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}22$$" ], "text/plain": [ "22" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(2,\\,1,\\,0,\\,-1,\\,2,\\,3,\\,4,\\,2,\\,3,\\,6\\right)$$" ], "text/plain": [ "(2, 1, 0, -1, 2, 3, 4, 2, 3, 6)" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{}$$" ], "text/plain": [ "salto" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$$" ], "text/plain": [ "ry" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{\\ \\ \\ Fase\\ I}$$" ], "text/plain": [ "FI" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$$" ], "text/plain": [ "ry" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {x}_{5} & {x}_{6} & {x}_{7} & {x}_{8} & {x}_{9} & {x}_{10} & {x}_{11} & {x}_{12} & {x}_{13} & {x}_{14} & {x}_{15} & {x}_{16} & {x}_{17} & {x}_{18} & {x}_{19} & {x}_{20} & {x}_{21} & {x}_{22} & {x}_{23} & {x}_{24} & {x}_{25} & {\\color{red}{t}}_{1} & {\\color{red}{t}}_{2} & {\\color{red}{t}}_{3} & {\\color{red}{t}}_{4} & {\\color{red}{t}}_{5} & {\\color{red}{t}}_{6} & {\\color{red}{t}}_{7} & {\\color{red}{t}}_{8} & {\\color{red}{t}}_{9} & {\\color{red}{t}}_{10} & {b} \\\\\n", "\\hline\n", " {\\color{red}{t}}_{1} & 1 & 1 & 1 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 \\\\\n", "{\\color{red}{t}}_{2} & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 \\\\\n", "{\\color{red}{t}}_{3} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 \\\\\n", "{\\color{red}{t}}_{4} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 \\\\\n", "{\\color{red}{t}}_{5} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 1 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 \\\\\n", "{\\color{red}{t}}_{6} & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 1 \\\\\n", "{\\color{red}{t}}_{7} & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 1 \\\\\n", "{\\color{red}{t}}_{8} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 1 \\\\\n", "{\\color{red}{t}}_{9} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 \\\\\n", "{\\color{red}{t}}_{10} & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 \\\\\n", "\\hline\n", " {W_{ind}} & -2 & -2 & -2 & -2 & -2 & -2 & -2 & -2 & -2 & -2 & -2 & -2 & -2 & -2 & -2 & -2 & -2 & -2 & -2 & -2 & -2 & -2 & -2 & -2 & -2 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 10\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 x21 x22 x23 x24 x25 t1 t2 t3 t4 t5 t6 t7 t8 t9 t10|rhs]\n", "[---+-------------------------------------------------------------------------------------------------------------------------------------------+---]\n", "[ t1| 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0| 1]\n", "[ t2| 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0| 1]\n", "[ t3| 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0| 1]\n", "[ t4| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0| 1]\n", "[ t5| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 1 0 0 0 0 0| 1]\n", "[ t6| 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0| 1]\n", "[ t7| 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0| 1]\n", "[ t8| 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0| 1]\n", "[ t9| 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0| 1]\n", "[t10| 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1| 1]\n", "[---+-------------------------------------------------------------------------------------------------------------------------------------------+---]\n", "[ W| -2 -2 -2 -2 -2 -2 -2 -2 -2 -2 -2 -2 -2 -2 -2 -2 -2 -2 -2 -2 -2 -2 -2 -2 -2 0 0 0 0 0 0 0 0 0 0| 10]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ " \n", " \n", "cambio( 1 , 1 )\n", "cambio( 6 , 6 )\n", "cambio( 1 , 2 )\n", "cambio( 2 , 7 )\n", "cambio( 7 , 11 )\n", "cambio( 1 , 3 )\n", "cambio( 3 , 8 )\n", "cambio( 6 , 16 )\n", "cambio( 8 , 12 )\n", "cambio( 1 , 4 )\n", "cambio( 2 , 9 )\n", "cambio( 4 , 13 )\n", "cambio( 7 , 21 )\n", "cambio( 9 , 17 )\n", "cambio( 1 , 5 )\n", "cambio( 3 , 10 )\n", "cambio( 5 , 14 )\n" ] }, { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {x}_{5} & {x}_{6} & {x}_{7} & {x}_{8} & {x}_{9} & {x}_{10} & {x}_{11} & {x}_{12} & {x}_{13} & {x}_{14} & {x}_{15} & {x}_{16} & {x}_{17} & {x}_{18} & {x}_{19} & {x}_{20} & {x}_{21} & {x}_{22} & {x}_{23} & {x}_{24} & {x}_{25} & {\\color{red}{t}}_{1} & {\\color{red}{t}}_{2} & {\\color{red}{t}}_{3} & {\\color{red}{t}}_{4} & {\\color{red}{t}}_{5} & {\\color{red}{t}}_{6} & {\\color{red}{t}}_{7} & {\\color{red}{t}}_{8} & {\\color{red}{t}}_{9} & {\\color{red}{t}}_{10} & {b} \\\\\n", "\\hline\n", " {x}_{5} & 1 & 1 & 1 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 \\\\\n", "{x}_{9} & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & -1 & -1 & -1 & 1 & 1 & 1 & 1 & 0 & 1 \\\\\n", "{x}_{10} & -1 & -1 & -1 & -1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 1 & 1 & 1 & -1 & -1 & -1 & -1 & 0 & 0 \\\\\n", "{x}_{13} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 1 \\\\\n", "{x}_{14} & -1 & -1 & -1 & 0 & 0 & -1 & -1 & -1 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 1 & -1 & -1 & -1 & 0 & 0 & 0 \\\\\n", "{x}_{16} & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & -1 & -1 & -1 & 0 & 0 & 0 & 0 & -1 & 1 & 0 & 0 & 0 & 0 & 0 \\\\\n", "{x}_{21} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 1 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 \\\\\n", "{x}_{12} & 1 & 1 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & -1 & -1 & 0 & 0 & -1 & -1 & -1 & 0 & 0 & 0 & -1 & -1 & 1 & 1 & 0 & 0 & 0 & 0 \\\\\n", "{x}_{17} & -1 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 1 & 1 & 0 & 0 & 0 & 1 & 1 & -1 & 0 & 0 & 0 & 0 & 1 \\\\\n", "{\\color{red}{t}}_{10} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & -1 & -1 & -1 & -1 & 1 & 1 & 1 & 1 & 1 & 0 \\\\\n", "\\hline\n", " {W_{ind}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 2 & 2 & 2 & 2 & 2 & 0 & 0 & 0 & 0 & 0 & 0\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 x21 x22 x23 x24 x25 t1 t2 t3 t4 t5 t6 t7 t8 t9 t10|rhs]\n", "[---+-------------------------------------------------------------------------------------------------------------------------------------------+---]\n", "[ x5| 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0| 1]\n", "[ x9| 1 1 1 1 0 1 1 1 1 0 0 0 0 0 -1 0 0 0 0 -1 0 0 0 0 -1 0 0 -1 -1 -1 1 1 1 1 0| 1]\n", "[x10| -1 -1 -1 -1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 1 1 1 1 -1 -1 -1 -1 0| 0]\n", "[x13| 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0| 1]\n", "[x14| -1 -1 -1 0 0 -1 -1 -1 0 0 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 1 1 1 -1 -1 -1 0 0| 0]\n", "[x16| 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 -1 -1 -1 -1 0 0 0 0 -1 1 0 0 0 0| 0]\n", "[x21| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 1 0 0 0 0 0| 1]\n", "[x12| 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 0 0 -1 -1 -1 0 0 -1 -1 -1 0 0 0 -1 -1 1 1 0 0 0| 0]\n", "[x17| -1 0 0 0 0 -1 0 0 0 0 -1 0 0 0 0 0 1 1 1 1 0 1 1 1 1 0 0 0 1 1 -1 0 0 0 0| 1]\n", "[t10| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 -1 -1 -1 -1 1 1 1 1 1| 0]\n", "[---+-------------------------------------------------------------------------------------------------------------------------------------------+---]\n", "[ W| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 0 0 0 0 0| 0]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "El problema de la fase I es óptimo y Wopt=0. Por tanto, el original es factible\n", "Preparemos el cuadro inicial de la fase II\n" ] }, { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$$" ], "text/plain": [ "ry" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{\\ \\ \\ Fase\\ II}$$" ], "text/plain": [ "FII" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$$" ], "text/plain": [ "ry" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrrrrrrrrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {x}_{5} & {x}_{6} & {x}_{7} & {x}_{8} & {x}_{9} & {x}_{10} & {x}_{11} & {x}_{12} & {x}_{13} & {x}_{14} & {x}_{15} & {x}_{16} & {x}_{17} & {x}_{18} & {x}_{19} & {x}_{20} & {x}_{21} & {x}_{22} & {x}_{23} & {x}_{24} & {x}_{25} & {b} \\\\\n", "\\hline\n", " {x}_{5} & 1 & 1 & 1 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 \\\\\n", "{x}_{9} & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 0 & 0 & -1 & 1 \\\\\n", "{x}_{10} & -1 & -1 & -1 & -1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 \\\\\n", "{x}_{13} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 1 \\\\\n", "{x}_{14} & -1 & -1 & -1 & 0 & 0 & -1 & -1 & -1 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 1 & 1 & 0 \\\\\n", "{x}_{16} & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & -1 & -1 & -1 & 0 \\\\\n", "{x}_{21} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 1 & 1 & 1 \\\\\n", "{x}_{12} & 1 & 1 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & -1 & -1 & 0 & 0 & -1 & -1 & -1 & 0 \\\\\n", "{x}_{17} & -1 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 1 & 1 & 1 \\\\\n", "\\hline\n", " {Z_{ind}} & 995 & -1 & -995 & 995 & 0 & 2 & 994 & -996 & 0 & 0 & 4 & 0 & 0 & 0 & 994 & 0 & 0 & -996 & 998 & 0 & 0 & -3 & -1001 & -3 & 989 & 1024\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 x21 x22 x23 x24 x25| rhs]\n", "[-----+-----------------------------------------------------------------------------------------------------------------------------------------------------+-----]\n", "[ x5| 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0| 1]\n", "[ x9| 1 1 1 1 0 1 1 1 1 0 0 0 0 0 -1 0 0 0 0 -1 0 0 0 0 -1| 1]\n", "[ x10| -1 -1 -1 -1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1| 0]\n", "[ x13| 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0| 1]\n", "[ x14| -1 -1 -1 0 0 -1 -1 -1 0 0 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1| 0]\n", "[ x16| 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 -1 -1 -1 -1| 0]\n", "[ x21| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1| 1]\n", "[ x12| 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 0 0 -1 -1 -1 0 0 -1 -1 -1| 0]\n", "[ x17| -1 0 0 0 0 -1 0 0 0 0 -1 0 0 0 0 0 1 1 1 1 0 1 1 1 1| 1]\n", "[-----+-----------------------------------------------------------------------------------------------------------------------------------------------------+-----]\n", "[ Z| 995 -1 -995 995 0 2 994 -996 0 0 4 0 0 0 994 0 0 -996 998 0 0 -3 -1001 -3 989| 1024]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "cambio( 4 , 23 )\n", "cambio( 7 , 22 )\n", "cambio( 1 , 2 )\n" ] }, { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrrrrrrrrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {x}_{5} & {x}_{6} & {x}_{7} & {x}_{8} & {x}_{9} & {x}_{10} & {x}_{11} & {x}_{12} & {x}_{13} & {x}_{14} & {x}_{15} & {x}_{16} & {x}_{17} & {x}_{18} & {x}_{19} & {x}_{20} & {x}_{21} & {x}_{22} & {x}_{23} & {x}_{24} & {x}_{25} & {b} \\\\\n", "\\hline\n", " {x}_{2} & 1 & 1 & 1 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 \\\\\n", "{x}_{9} & 0 & 0 & 0 & 0 & -1 & 1 & 1 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 0 & 0 & -1 & 0 \\\\\n", "{x}_{10} & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 1 \\\\\n", "{x}_{23} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 1 \\\\\n", "{x}_{14} & 0 & 0 & 0 & 1 & 1 & -1 & -1 & -1 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 1 & 1 & 1 \\\\\n", "{x}_{16} & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 1 \\\\\n", "{x}_{22} & 0 & 0 & -1 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 1 & 1 & 0 & 1 & 1 & 0 \\\\\n", "{x}_{12} & 0 & 0 & 0 & -1 & -1 & 1 & 1 & 1 & 0 & 0 & 1 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & -1 & 0 & 0 & 0 & -1 & -1 & 0 \\\\\n", "{x}_{17} & -1 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 1 & -1 & 0 & 0 & 0 & 0 & 0 \\\\\n", "\\hline\n", " {Z_{ind}} & 996 & 0 & 4 & 996 & 1 & 2 & 994 & 2 & 0 & 0 & 4 & 0 & 998 & 0 & 994 & 0 & 0 & 2 & 998 & 0 & 3 & 0 & 0 & 0 & 992 & 22\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 x21 x22 x23 x24 x25|rhs]\n", "[---+---------------------------------------------------------------------------------------------------+---]\n", "[ x2| 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0| 1]\n", "[ x9| 0 0 0 0 -1 1 1 1 1 0 0 0 0 0 -1 0 0 0 0 -1 0 0 0 0 -1| 0]\n", "[x10| 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1| 1]\n", "[x23| 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0| 1]\n", "[x14| 0 0 0 1 1 -1 -1 -1 0 0 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1| 1]\n", "[x16| 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0| 1]\n", "[x22| 0 0 -1 0 0 0 0 -1 0 0 0 0 -1 0 0 0 0 -1 0 0 1 1 0 1 1| 0]\n", "[x12| 0 0 0 -1 -1 1 1 1 0 0 1 1 1 0 0 0 0 0 -1 -1 0 0 0 -1 -1| 0]\n", "[x17| -1 0 0 0 0 -1 0 0 0 0 -1 0 0 0 0 0 1 1 1 1 -1 0 0 0 0| 0]\n", "[---+---------------------------------------------------------------------------------------------------+---]\n", "[ Z|996 0 4 996 1 2 994 2 0 0 4 0 998 0 994 0 0 2 998 0 3 0 0 0 992| 22]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "El problema es óptimo\n" ] } ], "source": [ "tipo='min' #max o min\n", "n=25 # número de variables x's\n", "m=10 # número de restricciones (distintas de las de signo)\n", "\n", "\n", "c=matrix(QQ,1,n,[1000, 6, 7, 1000, 8,\n", " 6,1000, 5, 4, 7,\n", " 7, 5, 1000, 3, 1000,\n", " 2, 4, 3, 1000, 5,\n", " 8, 7, 4, 5, 1000]\n", " ) # vector de costos\n", "\n", "A=matrix(QQ,m,n,[ # coeficientes de las variables x's\n", "[1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],\n", "[0,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],\n", "[0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0],\n", "[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0],\n", "[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1],\n", "[1,0,0,0,0,1,0,0,0,0,1,0,0,0,0,1,0,0,0,0,1,0,0,0,0],\n", "[0,1,0,0,0,0,1,0,0,0,0,1,0,0,0,0,1,0,0,0,0,1,0,0,0],\n", "[0,0,1,0,0,0,0,1,0,0,0,0,1,0,0,0,0,1,0,0,0,0,1,0,0],\n", "[0,0,0,1,0,0,0,0,1,0,0,0,0,1,0,0,0,0,1,0,0,0,0,1,0],\n", "[0,0,0,0,1,0,0,0,0,1,0,0,0,0,1,0,0,0,0,1,0,0,0,0,1]\n", "])\n", "\n", "b=matrix(QQ,m,1,[1,1,1,1,1,1,1,1,1,1]) # vector de la derecha\n", "\n", "\n", "\n", "######################################################\n", "############### VARIABLES DE HOLGURA ################\n", "\n", "\n", "h=matrix(ZZ,1,m,[0,0,0,0,0,0,0,0,0,0]) # variables de holgura: \n", " # Pon 1 si va sumando, \n", " # -1 si va restando y \n", " # 0 si no hay variable de holgura.\n", "\n", "#######################################################\n", "\n", "####################################################################\n", "############ HASTA AQUÍ LOS DATOS ################################\n", "####################################################################\n", "\n", "\n", "#load('https://sage.unex.es/501708/simplex2023Auto.sage')\n", "load('https://sage.unex.es/501708/simplex2023Auto_MC.sage')\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "SageMath 9.5", "language": "sage", "name": "sagemath" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.11.2" } }, "nbformat": 4, "nbformat_minor": 4 }