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"[---+-----------------------+---]\n", "[ s1| 1 0 0 1 0 0| 1]\n", "[ x2| 4 1 0 0 1 0| 5]\n", "[ x3| 0 0 1 0 -4 1| 5]\n", "[---+-----------------------+---]\n", "[ Z| -4 0 0 0 2 -1| 15]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "cambio( 2 , 5 )\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 1 & 0 & 0 & 1 & 0 & 0 & 1 \\\\\n", "{\\color{green}{s}}_{2} & 4 & 1 & 0 & 0 & 1 & 0 & 5 \\\\\n", "{x}_{3} & 16 & 4 & 1 & 0 & 0 & 1 & 25 \\\\\n", "\\hline\n", " {Z_{ind}} & -12 & -2 & 0 & 0 & 0 & -1 & 25\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {\\color{green}{s}}_{1} & 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x's\n", "[1,0,0],\n", "[4,1,0],\n", "[16,4, 1]\n", "])\n", "\n", "b=matrix(QQ,m,1,[1,5,25]) # vector de la derecha\n", "\n", "\n", "h=matrix(ZZ,1,m,[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", "t=matrix(ZZ,1,m,[0,0,0]) # 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=(4,5,6) # posición de la matriz identidad\n", "\n", "\n", " \n", " \n", "####################################################################\n", "############ HASTA AQUÍ LOS DATOS ################################\n", "####################################################################\n", "\n", "\n", "load('https://sage.unex.es/501708/simplex2023Auto.sage')\n", "\n", "#load('https://sage.unex.es/501708/simplex2023CompletamenteManual.sage')" ] }, { "cell_type": "code", "execution_count": 10, 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"text": [ "El problema es óptimo\n" ] } ], "source": [ "tipo='max' # Problema de tipo max o min\n", "\n", "n=3 # número de variables x's\n", "m=3 # número de restricciones (distintas de las de signo)\n", "\n", "c=matrix(QQ,1,n,[8,4,2] ) # vector de costos\n", "\n", "A=matrix(QQ,m,n,[ # coeficientes de las variables x's\n", "[1,0,0],\n", "[4,1,0],\n", "[16,4, 1]\n", "])\n", "\n", "b=matrix(QQ,m,1,[5,25,125]) # vector de la derecha\n", "\n", "\n", "h=matrix(ZZ,1,m,[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", "t=matrix(ZZ,1,m,[0,0,0]) # 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=(4,5,6) # posición de la matriz identidad\n", "\n", "\n", " \n", " \n", "####################################################################\n", "############ HASTA AQUÍ LOS DATOS 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20\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 s1 s2 s3|rhs]\n", "[---+-----------------------+---]\n", "[ x1| 1 0 0 1 0 0| 5]\n", "[ s2| 0 1 0 -2 1 0| 15]\n", "[ s3| 0 2 1 -4 0 1|105]\n", "[---+-----------------------+---]\n", "[ Z| 0 2 1 -4 0 0| 20]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "cambio(1,1)" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {b} \\\\\n", "\\hline\n", " {x}_{1} & 1 & 0 & 0 & 1 & 0 & 0 & 5 \\\\\n", "{x}_{2} & 0 & 1 & 0 & -2 & 1 & 0 & 15 \\\\\n", "{\\color{green}{s}}_{3} & 0 & 0 & 1 & 0 & -2 & 1 & 75 \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & 1 & 0 & -2 & 0 & 50\n", "\\end{array}\\right)$ " ], "text/latex": [ 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{\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {b} \\\\\n", "\\hline\n", " {x}_{1} & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 1 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & -2 & 1 & 0 & 0 & 98 \\\\\n", "{x}_{3} & 0 & 0 & 1 & 0 & 0 & -2 & 1 & 0 & 9800 \\\\\n", "{x}_{4} & 0 & 0 & 0 & 1 & 0 & 0 & -2 & 1 & 980000 \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & 0 & 0 & -8000 & -800 & -98 & -1 & 2068000\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {b} \\\\\n", "\\hline\n", " {x}_{1} & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 1 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & -2 & 1 & 0 & 0 & 98 \\\\\n", "{x}_{3} & 0 & 0 & 1 & 0 & 0 & -2 & 1 & 0 & 9800 \\\\\n", "{x}_{4} & 0 & 0 & 0 & 1 & 0 & 0 & -2 & 1 & 980000 \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & 0 & 0 & -8000 & -800 & -98 & -1 & 2068000\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3 s4| rhs]\n", "[-------+---------------------------------------------------------------+-------]\n", "[ x1| 1 0 0 0 1 0 0 0| 1]\n", "[ x2| 0 1 0 0 -2 1 0 0| 98]\n", "[ x3| 0 0 1 0 0 -2 1 0| 9800]\n", "[ x4| 0 0 0 1 0 0 -2 1| 980000]\n", "[-------+---------------------------------------------------------------+-------]\n", "[ Z| 0 0 0 0 -8000 -800 -98 -1|2068000]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "El problema es óptimo\n" ] } ], "source": [ "tipo='max' # Problema de tipo max o min\n", "\n", "n=4 # número de variables x's\n", "m=4 # número de restricciones (distintas de las de signo)\n", "\n", "c=matrix(QQ,1,n,[10000,1000,100,1] ) # vector de costos\n", "\n", "A=matrix(QQ,m,n,[ # coeficientes de las variables x's\n", "[1,0,0,0],\n", "[2,1,0,0],\n", "[4,2, 1,0],\n", "[8,4,2,1]\n", "])\n", "\n", "b=matrix(QQ,m,1,[1,100,10000, 1000000]) # vector de la derecha\n", "\n", "\n", "h=matrix(ZZ,1,m,[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", "t=matrix(ZZ,1,m,[0,0,0,0]) # 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=(5,6,7,8) # posición de la matriz identidad\n", "\n", "\n", " \n", " \n", "####################################################################\n", "############ HASTA AQUÍ LOS DATOS ################################\n", "####################################################################\n", "\n", "\n", "load('https://sage.unex.es/501708/simplex2023Auto.sage')\n", "\n", "#load('https://sage.unex.es/501708/simplex2023CompletamenteManual.sage')" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], 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