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"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{red}{t}}_{1} & {\\color{red}{t}}_{2} & {b} \\\\\n", "\\hline\n", " {\\color{red}{t}}_{1} & -1 & -3 & 2 & -3 & -1 & 0 & 1 & 0 & 5 \\\\\n", "{\\color{red}{t}}_{2} & -1 & 1 & -2 & 1 & 0 & -1 & 0 & 1 & 7 \\\\\n", "\\hline\n", " {W_{ind}} & 2 & 2 & 0 & 2 & 1 & 1 & 0 & 0 & 12\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 t1 t2|rhs]\n", "[---+-------------------------------+---]\n", "[ t1| -1 -3 2 -3 -1 0 1 0| 5]\n", "[ t2| -1 1 -2 1 0 -1 0 1| 7]\n", "[---+-------------------------------+---]\n", "[ W| 2 2 0 2 1 1 0 0| 12]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "tipo='min' # max o min\n", "\n", "n=4 # número de variables x's\n", "m=2 # número de restricciones (distintas de las de signo)\n", "\n", "c=matrix(QQ,1,n,[0,-2,2,3] ) # vector de costos\n", 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"metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": 20, "id": "3da01c91", "metadata": {}, "outputs": [ { "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": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{l}\n", "\\begin{array}{lcrcrcrcl}\n", " \\min \\mspace{-6mu}&\\mspace{-6mu} - \\mspace{-6mu}&\\mspace{-6mu} 2 x_{1} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 2 x_{2} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 3 x_{3} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\\\\n", " \\mspace{-6mu}&\\mspace{-6mu} - \\mspace{-6mu}&\\mspace{-6mu} x_{1} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} x_{2} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} x_{3} \\mspace{-6mu}&\\mspace{-6mu} \\geq \\mspace{-6mu}&\\mspace{-6mu} 16 \\\\\n", " \\mspace{-6mu}&\\mspace{-6mu} - \\mspace{-6mu}&\\mspace{-6mu} x_{1} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 2 x_{2} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 2 x_{3} \\mspace{-6mu}&\\mspace{-6mu} \\geq \\mspace{-6mu}&\\mspace{-6mu} 12 \\\\\n", "\\end{array} \\\\\n", "x_{1}, x_{2}, x_{3} \\geq 0\n", "\\end{array}$$" ], "text/plain": [ "LP problem (use 'view(...)' or '%display typeset' for details)" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}32$$" ], "text/plain": [ "32" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(0,\\,16,\\,0\\right)$$" ], "text/plain": [ "(0, 16, 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": [ "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": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{red}{t}}_{1} & {\\color{red}{t}}_{2} & {b} \\\\\n", "\\hline\n", " {\\color{red}{t}}_{1} & -1 & 1 & 1 & -1 & 0 & 1 & 0 & 16 \\\\\n", "{\\color{red}{t}}_{2} & -1 & 2 & 2 & 0 & -1 & 0 & 1 & 12 \\\\\n", "\\hline\n", " {W_{ind}} & 2 & -3 & -3 & 1 & 1 & 0 & 0 & 28\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 s1 s2 t1 t2|rhs]\n", "[---+---------------------------+---]\n", "[ t1| -1 1 1 -1 0 1 0| 16]\n", "[ t2| -1 2 2 0 -1 0 1| 12]\n", "[---+---------------------------+---]\n", "[ W| 2 -3 -3 1 1 0 0| 28]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "tipo='min' # max o min\n", "\n", "n=3 # número de variables x's\n", "m=2 # número de restricciones (distintas de las de signo)\n", "\n", "c=matrix(QQ,1,n,[-2,2,3] ) # vector de costos\n", "\n", "A=matrix(QQ,m,n,[ # coeficientes de las variables x's\n", "[-1,1,1],\n", "[-1,2,2]\n", "])\n", "\n", "b=matrix(QQ,m,1,[16,12]) # vector de la derecha\n", "\n", "\n", "######################################################\n", "############### VARIABLES DE HOLGURA ################\n", "\n", "\n", "h=matrix(ZZ,1,m,[-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", "t=matrix(ZZ,1,m,[1,1])\n", "\n", "colId=(6,7)\n", "\n", "\n", "\n", "\n", "\n", "####################################################################\n", "############ HASTA AQUÍ LOS DATOS ################################\n", "####################################################################\n", "\n", "\n", "\n", "load('https://sage.unex.es/501708/simplex2023CompletamenteManual.sage')\n", "\n", "#load('https://sage.unex.es/501708/simplex2023Auto.sage')" ] }, { "cell_type": "code", "execution_count": 21, "id": "91036c86", "metadata": {}, "outputs": [], "source": [ "#cambio(2,2);cambio(1,5);tt=[0,0]; faseII(0,tt)" ] }, { "cell_type": "code", "execution_count": 22, "id": "1f946002", "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ 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{ "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{red}{t}}_{1} & {\\color{red}{t}}_{2} & {b} \\\\\n", "\\hline\n", " {\\color{red}{t}}_{1} & -\\frac{1}{2} & 0 & 0 & -1 & \\frac{1}{2} & 1 & -\\frac{1}{2} & 10 \\\\\n", "{x}_{3} & -\\frac{1}{2} & 1 & 1 & 0 & -\\frac{1}{2} & 0 & \\frac{1}{2} & 6 \\\\\n", "\\hline\n", " {W_{ind}} & \\frac{1}{2} & 0 & 0 & 1 & -\\frac{1}{2} & 0 & \\frac{3}{2} & 10\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 s1 s2 t1 t2| rhs]\n", "[----+----------------------------------+----]\n", "[ t1|-1/2 0 0 -1 1/2 1 -1/2| 10]\n", "[ x3|-1/2 1 1 0 -1/2 0 1/2| 6]\n", "[----+----------------------------------+----]\n", "[ W| 1/2 0 0 1 -1/2 0 3/2| 10]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "cambio(2,3)" ] }, { "cell_type": "code", "execution_count": 6, "id": "6349d4da", "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{2} & -1 & 0 & 0 & -2 & 1 & 20 \\\\\n", "{x}_{2} & -1 & 1 & 1 & -1 & 0 & 16 \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & 1 & 2 & 0 & 32\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 s1 s2|rhs]\n", "[---+-------------------+---]\n", "[ s2| -1 0 0 -2 1| 20]\n", "[ x2| -1 1 1 -1 0| 16]\n", "[---+-------------------+---]\n", "[ Z| 0 0 1 2 0| 32]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "tt=[0,0]; faseII(0,tt)" ] }, { "cell_type": "code", "execution_count": null, "id": "3ea72535", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": 7, "id": "6bcca2b4", "metadata": {}, "outputs": [ { "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": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{l}\n", "\\begin{array}{lcrcrcrcl}\n", " \\min \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} 0 \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\\\\n", " \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} 2 x_{1} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 3 x_{2} \\mspace{-6mu}&\\mspace{-6mu} + 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"display_data" }, { "data": { "text/html": [ "" ], "text/latex": [ "$$\\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}}{===================================}$$" ], "text/plain": [ "ry" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {\\color{red}{t}}_{1} & {\\color{red}{t}}_{2} & {b} \\\\\n", "\\hline\n", " {\\color{red}{t}}_{1} & 2 & 3 & 4 & 1 & 0 & 17 \\\\\n", "{\\color{red}{t}}_{2} & -1 & 2 & 3 & 0 & 1 & 5 \\\\\n", "\\hline\n", " {W_{ind}} & -1 & -5 & -7 & 0 & 0 & 22\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 t1 t2|rhs]\n", "[---+-------------------+---]\n", "[ t1| 2 3 4 1 0| 17]\n", "[ t2| -1 2 3 0 1| 5]\n", "[---+-------------------+---]\n", "[ W| -1 -5 -7 0 0| 22]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "tipo='min' # max o min\n", "\n", "n=3 # número de variables x's\n", "m=2 # número de restricciones (distintas de las de signo)\n", "\n", "c=matrix(QQ,1,n,[0,0,0] ) # vector de costos\n", "\n", "A=matrix(QQ,m,n,[ # coeficientes de las variables x's\n", "[2,3,4],\n", "[-1,2,3]\n", "])\n", "\n", "b=matrix(QQ,m,1,[17,5]) # vector de la derecha\n", "\n", "\n", "######################################################\n", "############### VARIABLES DE HOLGURA ################\n", "\n", "\n", "h=matrix(ZZ,1,m,[0,0]) # variables de holgura: \n", " # Pon 1 si va sumando, \n", " # -1 si va restando y \n", " # 0 si no hay variable de holgura.\n", "t=matrix(ZZ,1,m,[1,1])\n", "\n", "colId=(4,5)\n", "\n", "\n", "\n", "\n", "\n", "####################################################################\n", "############ HASTA AQUÍ LOS DATOS ################################\n", "####################################################################\n", "\n", "\n", "\n", "load('https://sage.unex.es/501708/simplex2023CompletamenteManual.sage')\n", "\n", "#load('https://sage.unex.es/501708/simplex2023Auto.sage')" ] }, { "cell_type": "code", "execution_count": 8, "id": "c7e7d901", "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {\\color{red}{t}}_{1} & {\\color{red}{t}}_{2} & {b} \\\\\n", "\\hline\n", " {\\color{red}{t}}_{1} & \\frac{10}{3} & \\frac{1}{3} & 0 & 1 & -\\frac{4}{3} & \\frac{31}{3} \\\\\n", "{x}_{3} & -\\frac{1}{3} & \\frac{2}{3} & 1 & 0 & \\frac{1}{3} & \\frac{5}{3} \\\\\n", "\\hline\n", " {W_{ind}} & -\\frac{10}{3} & 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