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"text/plain": [ "FI" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$$" ], "text/plain": [ "ry" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{red}{t}}_{2} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 1 & 1 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 1 \\\\\n", "{\\color{red}{t}}_{2} & 1 & 1 & 1 & 0 & -1 & 0 & 0 & 0 & 1 & 1 \\\\\n", "{\\color{green}{s}}_{3} & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 1 \\\\\n", "{\\color{green}{s}}_{4} & 0 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 2 \\\\\n", "{\\color{green}{s}}_{5} & 1 & 1 & 2 & 0 & 0 & 0 & 0 & 1 & 0 & 2 \\\\\n", "\\hline\n", " {W_{ind}} & -1 & -1 & -1 & 0 & 1 & 0 & 0 & 0 & 0 & 1\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{red}{t}}_{2} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 1 & 1 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 1 \\\\\n", "{\\color{red}{t}}_{2} & 1 & 1 & 1 & 0 & -1 & 0 & 0 & 0 & 1 & 1 \\\\\n", "{\\color{green}{s}}_{3} & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 1 \\\\\n", "{\\color{green}{s}}_{4} & 0 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 2 \\\\\n", "{\\color{green}{s}}_{5} & 1 & 1 & 2 & 0 & 0 & 0 & 0 & 1 & 0 & 2 \\\\\n", "\\hline\n", " {W_{ind}} & -1 & -1 & -1 & 0 & 1 & 0 & 0 & 0 & 0 & 1\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 s1 s2 s3 s4 s5 t2|rhs]\n", "[---+-----------------------------------+---]\n", "[ s1| 1 1 1 1 0 0 0 0 0| 1]\n", "[ t2| 1 1 1 0 -1 0 0 0 1| 1]\n", "[ s3| 1 0 1 0 0 1 0 0 0| 1]\n", "[ s4| 0 0 1 0 0 0 1 0 0| 2]\n", "[ s5| 1 1 2 0 0 0 0 1 0| 2]\n", "[---+-----------------------------------+---]\n", "[ W| -1 -1 -1 0 1 0 0 0 0| 1]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "cambio( 1 , 1 )\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{red}{t}}_{2} & {b} \\\\\n", "\\hline\n", " {x}_{1} & 1 & 1 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 1 \\\\\n", "{\\color{red}{t}}_{2} & 0 & 0 & 0 & -1 & -1 & 0 & 0 & 0 & 1 & 0 \\\\\n", "{\\color{green}{s}}_{3} & 0 & -1 & 0 & -1 & 0 & 1 & 0 & 0 & 0 & 0 \\\\\n", "{\\color{green}{s}}_{4} & 0 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 2 \\\\\n", "{\\color{green}{s}}_{5} & 0 & 0 & 1 & -1 & 0 & 0 & 0 & 1 & 0 & 1 \\\\\n", "\\hline\n", " {W_{ind}} & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{red}{t}}_{2} & {b} \\\\\n", "\\hline\n", " {x}_{1} & 1 & 1 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 1 \\\\\n", "{\\color{red}{t}}_{2} & 0 & 0 & 0 & -1 & -1 & 0 & 0 & 0 & 1 & 0 \\\\\n", "{\\color{green}{s}}_{3} & 0 & -1 & 0 & -1 & 0 & 1 & 0 & 0 & 0 & 0 \\\\\n", "{\\color{green}{s}}_{4} & 0 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 2 \\\\\n", "{\\color{green}{s}}_{5} & 0 & 0 & 1 & -1 & 0 & 0 & 0 & 1 & 0 & 1 \\\\\n", "\\hline\n", " {W_{ind}} & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 s1 s2 s3 s4 s5 t2|rhs]\n", "[---+-----------------------------------+---]\n", "[ x1| 1 1 1 1 0 0 0 0 0| 1]\n", "[ t2| 0 0 0 -1 -1 0 0 0 1| 0]\n", "[ s3| 0 -1 0 -1 0 1 0 0 0| 0]\n", "[ s4| 0 0 1 0 0 0 1 0 0| 2]\n", "[ s5| 0 0 1 -1 0 0 0 1 0| 1]\n", "[---+-----------------------------------+---]\n", "[ W| 0 0 0 1 1 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": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{red}{t}}_{2} & {b} \\\\\n", "\\hline\n", " {x}_{1} & 1 & 1 & 1 & 0 & -1 & 0 & 0 & 0 & 1 & 1 \\\\\n", "{\\color{green}{s}}_{1} & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & -1 & 0 \\\\\n", "{\\color{green}{s}}_{3} & 0 & -1 & 0 & 0 & 1 & 1 & 0 & 0 & -1 & 0 \\\\\n", "{\\color{green}{s}}_{4} & 0 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 2 \\\\\n", "{\\color{green}{s}}_{5} & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 1 & -1 & 1 \\\\\n", "\\hline\n", " {W_{ind}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrr|r}\n", "{Basic} & {x}_{1} & 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1 & 0 & 0 & 0 & 0 \\\\\n", "{\\color{green}{s}}_{3} & 0 & -1 & 0 & -1 & 0 & 1 & 0 & 0 & 0 \\\\\n", "{\\color{green}{s}}_{4} & 0 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 2 \\\\\n", "{\\color{green}{s}}_{5} & 0 & 0 & 1 & -1 & 0 & 0 & 0 & 1 & 1 \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & 2 & 1 & 0 & 0 & 0 & 0 & -1\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 s1 s2 s3 s4 s5|rhs]\n", "[---+-------------------------------+---]\n", "[ x1| 1 1 1 1 0 0 0 0| 1]\n", "[ s2| 0 0 0 1 1 0 0 0| 0]\n", "[ s3| 0 -1 0 -1 0 1 0 0| 0]\n", "[ s4| 0 0 1 0 0 0 1 0| 2]\n", "[ s5| 0 0 1 -1 0 0 0 1| 1]\n", "[---+-------------------------------+---]\n", "[ Z| 0 0 2 1 0 0 0 0| -1]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "cambio( 1 , 3 )\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} 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& -1 & 0 & 1 & 0 & 0 & 0 \\\\\n", "{\\color{green}{s}}_{4} & -1 & -1 & 0 & -1 & 0 & 0 & 1 & 0 & 1 \\\\\n", "{\\color{green}{s}}_{5} & -1 & -1 & 0 & -2 & 0 & 0 & 0 & 1 & 0 \\\\\n", "\\hline\n", " {Z_{ind}} & -2 & -2 & 0 & -1 & 0 & 0 & 0 & 0 & 1\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 s1 s2 s3 s4 s5|rhs]\n", "[---+-------------------------------+---]\n", "[ x3| 1 1 1 1 0 0 0 0| 1]\n", "[ s2| 0 0 0 1 1 0 0 0| 0]\n", "[ s3| 0 -1 0 -1 0 1 0 0| 0]\n", "[ s4| -1 -1 0 -1 0 0 1 0| 1]\n", "[ s5| -1 -1 0 -2 0 0 0 1| 0]\n", "[---+-------------------------------+---]\n", "[ Z| -2 -2 0 -1 0 0 0 0| 1]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "El problema es óptimo\n" ] } ], "source": [ "tipo='max' # max o min\n", "\n", "n=3 # número de variables x's\n", "m=5 # número de restricciones (distintas de las de signo)\n", "\n", "c=matrix(QQ,1,n,[-1,-1,1] ) # vector de costos\n", "\n", "A=matrix(QQ,m,n,[ # coeficientes de las variables x's\n", "[1,1,1],\n", "[1,1,1],\n", "[1,0,1],\n", "[0,0,1],\n", "[1,1,2]\n", "])\n", "\n", "b=matrix(QQ,m,1,[1,1,1,2,2]) # vector de la derecha\n", "\n", "\n", "h=matrix(ZZ,1,m,[1,-1,1,1,1]) # variables de holgura: \n", " # Pon 1 si va sumando, \n", " # -1 si va restando y \n", " # 0 si no hay variable de holgura.\n", "#######################################################\n", "\n", "load('https://sage.unex.es/501708/simplex2023Auto.sage')\n", "#load('https://sage.unex.es/501708/simplex2023AutoREVISED.sage')\n", "#load('https://sage.unex.es/501708/simplex2023AutoRevisada.sage')" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}8$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}8$$" ], "text/plain": [ "8" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "\n", "show(nvar)" ] }, { "cell_type": "code", "execution_count": null, 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