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"x_{1}, x_{2}, x_{3}, x_{4}, x_{5}, x_{6} \\geq 0\n", "\\end{array}$$" ], "text/plain": [ "LP problem (use 'view(...)' or '%display typeset' for details)" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}+\\infty$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}+\\infty$$" ], "text/plain": [ "+Infinity" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{None}$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{None}$$" ], "text/plain": [ "None" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$$" ], "text/plain": [ "ry" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}{}$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{}$$" ], "text/plain": [ "salto" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$$" ], "text/plain": [ "ry" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {x}_{5} & {x}_{6} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{3} & {\\color{red}{t}}_{2} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 2 & 2 & 1 & 2 & -1 & 1 & 1 & 0 & 0 & 10 \\\\\n", "{\\color{red}{t}}_{2} & 1 & 5 & -1 & -1 & 1 & -1 & 0 & 0 & 1 & 15 \\\\\n", "{\\color{green}{s}}_{3} & -1 & 3 & 2 & -2 & -1 & 1 & 0 & 1 & 0 & 25 \\\\\n", "\\hline\n", " {W_{ind}} & -1 & -5 & 1 & 1 & -1 & 1 & 0 & 0 & 0 & 15\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {x}_{5} & {x}_{6} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{3} & {\\color{red}{t}}_{2} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 2 & 2 & 1 & 2 & -1 & 1 & 1 & 0 & 0 & 10 \\\\\n", "{\\color{red}{t}}_{2} & 1 & 5 & -1 & -1 & 1 & -1 & 0 & 0 & 1 & 15 \\\\\n", "{\\color{green}{s}}_{3} & -1 & 3 & 2 & -2 & -1 & 1 & 0 & 1 & 0 & 25 \\\\\n", "\\hline\n", " {W_{ind}} & -1 & -5 & 1 & 1 & -1 & 1 & 0 & 0 & 0 & 15\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 x5 x6 s1 s3 t2|rhs]\n", "[---+-----------------------------------+---]\n", "[ s1| 2 2 1 2 -1 1 1 0 0| 10]\n", "[ t2| 1 5 -1 -1 1 -1 0 0 1| 15]\n", "[ s3| -1 3 2 -2 -1 1 0 1 0| 25]\n", "[---+-----------------------------------+---]\n", "[ W| -1 -5 1 1 -1 1 0 0 0| 15]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "tipo ='max' # Problema de tipo max o min\n", "\n", "n=6 # número de variables x's\n", "m=3 # número de restricciones (distintas de las de signo)\n", "\n", "c=matrix(QQ,1,n,[3,3,3,1,5,2] ) # vector de costos\n", "\n", "A=matrix(QQ,m,n,[ # coeficientes de las variables x's\n", "[2,2,1,2,-1,1],\n", "[1,5,-1,-1,1,-1],\n", "[-1,3,2,-2,-1,1]\n", "])\n", "\n", "b=matrix(QQ,m,1,[10,15,25]) # vector de la derecha\n", "\n", "\n", "h=matrix(ZZ,1,m,[1,0,1]) # variables de holgura: \n", " # Pon 1 si va sumando, \n", " # -1 si va restando y \n", " \n", "t=matrix(ZZ,1,m,[0,1,0]) # variables artificiales: \n", " # pon 1 si utilizas variable artificial en la fila i-ésima\n", " # 0 si no utilizas variable artificial en la fila i-ésima\n", "\n", "colId=(7,9,8) # posición de la matriz identidad\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/simplex2023CompletamenteManual.sage')\n" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {x}_{5} & {x}_{6} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{3} & {\\color{red}{t}}_{2} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & \\frac{8}{5} & 0 & \\frac{7}{5} & \\frac{12}{5} & -\\frac{7}{5} & \\frac{7}{5} & 1 & 0 & -\\frac{2}{5} & 4 \\\\\n", "{x}_{2} & \\frac{1}{5} & 1 & -\\frac{1}{5} & -\\frac{1}{5} & \\frac{1}{5} & -\\frac{1}{5} & 0 & 0 & \\frac{1}{5} & 3 \\\\\n", "{\\color{green}{s}}_{3} & -\\frac{8}{5} & 0 & \\frac{13}{5} & -\\frac{7}{5} & -\\frac{8}{5} & \\frac{8}{5} & 0 & 1 & -\\frac{3}{5} & 16 \\\\\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} & {x}_{2} & {x}_{3} & {x}_{4} & {x}_{5} & {x}_{6} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{3} & {\\color{red}{t}}_{2} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & \\frac{8}{5} & 0 & \\frac{7}{5} & \\frac{12}{5} & -\\frac{7}{5} & \\frac{7}{5} & 1 & 0 & -\\frac{2}{5} & 4 \\\\\n", "{x}_{2} & \\frac{1}{5} & 1 & -\\frac{1}{5} & -\\frac{1}{5} & \\frac{1}{5} & -\\frac{1}{5} & 0 & 0 & \\frac{1}{5} & 3 \\\\\n", "{\\color{green}{s}}_{3} & -\\frac{8}{5} & 0 & \\frac{13}{5} & -\\frac{7}{5} & -\\frac{8}{5} & \\frac{8}{5} & 0 & 1 & -\\frac{3}{5} & 16 \\\\\n", "\\hline\n", " {W_{ind}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 x5 x6 s1 s3 t2| rhs]\n", "[----+--------------------------------------------+----]\n", "[ s1| 8/5 0 7/5 12/5 -7/5 7/5 1 0 -2/5| 4]\n", "[ x2| 1/5 1 -1/5 -1/5 1/5 -1/5 0 0 1/5| 3]\n", "[ s3|-8/5 0 13/5 -7/5 -8/5 8/5 0 1 -3/5| 16]\n", "[----+--------------------------------------------+----]\n", "[ W| 0 0 0 0 0 0 0 0 1| 0]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "cambio(2,2)" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {x}_{5} & {x}_{6} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{3} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & \\frac{8}{5} & 0 & \\frac{7}{5} & \\frac{12}{5} & -\\frac{7}{5} & \\frac{7}{5} & 1 & 0 & 4 \\\\\n", "{x}_{2} & \\frac{1}{5} & 1 & -\\frac{1}{5} & -\\frac{1}{5} & \\frac{1}{5} & -\\frac{1}{5} & 0 & 0 & 3 \\\\\n", "{\\color{green}{s}}_{3} & -\\frac{8}{5} & 0 & \\frac{13}{5} & -\\frac{7}{5} & -\\frac{8}{5} & \\frac{8}{5} & 0 & 1 & 16 \\\\\n", "\\hline\n", " {Z_{ind}} & \\frac{12}{5} & 0 & \\frac{18}{5} & \\frac{8}{5} & \\frac{22}{5} & \\frac{13}{5} & 0 & 0 & 9\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {x}_{5} & {x}_{6} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{3} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & \\frac{8}{5} & 0 & \\frac{7}{5} & \\frac{12}{5} & -\\frac{7}{5} & \\frac{7}{5} & 1 & 0 & 4 \\\\\n", "{x}_{2} & \\frac{1}{5} & 1 & -\\frac{1}{5} & -\\frac{1}{5} & \\frac{1}{5} & -\\frac{1}{5} & 0 & 0 & 3 \\\\\n", "{\\color{green}{s}}_{3} & -\\frac{8}{5} & 0 & \\frac{13}{5} & -\\frac{7}{5} & -\\frac{8}{5} & \\frac{8}{5} & 0 & 1 & 16 \\\\\n", "\\hline\n", " {Z_{ind}} & \\frac{12}{5} & 0 & \\frac{18}{5} & \\frac{8}{5} & \\frac{22}{5} & \\frac{13}{5} & 0 & 0 & 9\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 x5 x6 s1 s3| rhs]\n", "[----+---------------------------------------+----]\n", "[ s1| 8/5 0 7/5 12/5 -7/5 7/5 1 0| 4]\n", "[ 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$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {x}_{5} & {x}_{6} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{3} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 3 & 7 & 0 & 1 & 0 & 0 & 1 & 0 & 25 \\\\\n", "{x}_{5} & 1 & 13 & 0 & -4 & 1 & -1 & 0 & 1 & 55 \\\\\n", "{x}_{3} & 0 & 8 & 1 & -3 & 0 & 0 & 0 & 1 & 40 \\\\\n", "\\hline\n", " {Z_{ind}} & -2 & -86 & 0 & 30 & 0 & 7 & 0 & -8 & 395\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {x}_{5} & {x}_{6} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{3} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 3 & 7 & 0 & 1 & 0 & 0 & 1 & 0 & 25 \\\\\n", "{x}_{5} & 1 & 13 & 0 & -4 & 1 & -1 & 0 & 1 & 55 \\\\\n", "{x}_{3} & 0 & 8 & 1 & -3 & 0 & 0 & 0 & 1 & 40 \\\\\n", "\\hline\n", " {Z_{ind}} & -2 & -86 & 0 & 30 & 0 & 7 & 0 & -8 & 395\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 x5 x6 s1 s3|rhs]\n", "[---+-------------------------------+---]\n", "[ s1| 3 7 0 1 0 0 1 0| 25]\n", "[ x5| 1 13 0 -4 1 -1 0 1| 55]\n", "[ x3| 0 8 1 -3 0 0 0 1| 40]\n", "[---+-------------------------------+---]\n", "[ Z| -2 -86 0 30 0 7 0 -8|395]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "cambio(3,3)" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {x}_{5} & {x}_{6} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{3} & {b} \\\\\n", "\\hline\n", " {x}_{4} & 3 & 7 & 0 & 1 & 0 & 0 & 1 & 0 & 25 \\\\\n", "{x}_{5} & 13 & 41 & 0 & 0 & 1 & -1 & 4 & 1 & 155 \\\\\n", "{x}_{3} & 9 & 29 & 1 & 0 & 0 & 0 & 3 & 1 & 115 \\\\\n", "\\hline\n", " {Z_{ind}} & -92 & -296 & 0 & 0 & 0 & 7 & -30 & -8 & 1145\n", 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