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"display_data" }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}{\\ \\ \\ Fase\\ I}$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{\\ \\ \\ Fase\\ I}$$" ], "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": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{red}{t}}_{5} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & \\frac{5}{2} & 3 & 1 & 0 & 0 & 0 & 0 & 0 & 4500 \\\\\n", "{\\color{green}{s}}_{2} & 3 & \\frac{3}{5} & 0 & 1 & 0 & 0 & 0 & 0 & 3400 \\\\\n", "{\\color{green}{s}}_{3} & 14 & 10 & 0 & 0 & 1 & 0 & 0 & 0 & 20000 \\\\\n", "{\\color{green}{s}}_{4} & 1 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 1700 \\\\\n", "{\\color{red}{t}}_{5} & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 1 & 600 \\\\\n", "\\hline\n", " {W_{ind}} & -1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 600\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{red}{t}}_{5} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & \\frac{5}{2} & 3 & 1 & 0 & 0 & 0 & 0 & 0 & 4500 \\\\\n", "{\\color{green}{s}}_{2} & 3 & \\frac{3}{5} & 0 & 1 & 0 & 0 & 0 & 0 & 3400 \\\\\n", "{\\color{green}{s}}_{3} & 14 & 10 & 0 & 0 & 1 & 0 & 0 & 0 & 20000 \\\\\n", "{\\color{green}{s}}_{4} & 1 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 1700 \\\\\n", "{\\color{red}{t}}_{5} & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 1 & 600 \\\\\n", "\\hline\n", " {W_{ind}} & -1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 600\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 s1 s2 s3 s4 s5 t5| rhs]\n", "[-----+-----------------------------------------------+-----]\n", "[ s1| 5/2 3 1 0 0 0 0 0| 4500]\n", "[ s2| 3 3/5 0 1 0 0 0 0| 3400]\n", "[ s3| 14 10 0 0 1 0 0 0|20000]\n", "[ s4| 1 1 0 0 0 1 0 0| 1700]\n", "[ t5| 1 0 0 0 0 0 -1 1| 600]\n", "[-----+-----------------------------------------------+-----]\n", "[ W| -1 0 0 0 0 0 1 0| 600]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "cambio( 5 , 1 )\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{red}{t}}_{5} & {b} 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"{\\color{green}{s}}_{3} & 0 & 10 & 0 & 0 & 1 & 0 & 14 & -14 & 11600 \\\\\n", "{\\color{green}{s}}_{4} & 0 & 1 & 0 & 0 & 0 & 1 & 1 & -1 & 1100 \\\\\n", "{x}_{1} & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 1 & 600 \\\\\n", "\\hline\n", " {W_{ind}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 s1 s2 s3 s4 s5 t5| rhs]\n", "[-----+-----------------------------------------------+-----]\n", "[ s1| 0 3 1 0 0 0 5/2 -5/2| 3000]\n", "[ s2| 0 3/5 0 1 0 0 3 -3| 1600]\n", "[ s3| 0 10 0 0 1 0 14 -14|11600]\n", "[ s4| 0 1 0 0 0 1 1 -1| 1100]\n", "[ x1| 1 0 0 0 0 0 -1 1| 600]\n", "[-----+-----------------------------------------------+-----]\n", "[ W| 0 0 0 0 0 0 0 1| 0]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "El problema de la fase I es óptimo y Wopt=0. Por tanto, el original es factible\n", "Preparemos el cuadro inicial de la fase II\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$$" ], "text/plain": [ "ry" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}{\\ \\ \\ Fase\\ II}$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{\\ \\ \\ Fase\\ II}$$" ], "text/plain": [ "FII" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$$" ], "text/plain": [ "ry" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " 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{\\color{green}{s}}_{1} & 0 & 3 & 1 & 0 & 0 & 0 & \\frac{5}{2} & 3000 \\\\\n", "{\\color{green}{s}}_{2} & 0 & \\frac{3}{5} & 0 & 1 & 0 & 0 & 3 & 1600 \\\\\n", "{\\color{green}{s}}_{3} & 0 & 10 & 0 & 0 & 1 & 0 & 14 & 11600 \\\\\n", "{\\color{green}{s}}_{4} & 0 & 1 & 0 & 0 & 0 & 1 & 1 & 1100 \\\\\n", "{x}_{1} & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 600 \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 200 & 0 & 0 & 0 & 0 & 220 & 132000\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 s1 s2 s3 s4 s5| rhs]\n", "[------+------------------------------------------------+------]\n", "[ s1| 0 3 1 0 0 0 5/2| 3000]\n", "[ s2| 0 3/5 0 1 0 0 3| 1600]\n", "[ s3| 0 10 0 0 1 0 14| 11600]\n", "[ s4| 0 1 0 0 0 1 1| 1100]\n", "[ x1| 1 0 0 0 0 0 -1| 600]\n", "[------+------------------------------------------------+------]\n", "[ Z| 0 200 0 0 0 0 220|132000]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "cambio( 2 , 7 )\n" ] }, { "data": { 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"{Basic} & {x}_{1} & {x}_{2} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 0 & \\frac{5}{2} & 1 & -\\frac{5}{6} & 0 & 0 & 0 & \\frac{5000}{3} \\\\\n", "{\\color{green}{s}}_{5} & 0 & \\frac{1}{5} & 0 & \\frac{1}{3} & 0 & 0 & 1 & \\frac{1600}{3} \\\\\n", "{\\color{green}{s}}_{3} & 0 & \\frac{36}{5} & 0 & -\\frac{14}{3} & 1 & 0 & 0 & \\frac{12400}{3} \\\\\n", "{\\color{green}{s}}_{4} & 0 & \\frac{4}{5} & 0 & -\\frac{1}{3} & 0 & 1 & 0 & \\frac{1700}{3} \\\\\n", "{x}_{1} & 1 & \\frac{1}{5} & 0 & \\frac{1}{3} & 0 & 0 & 0 & \\frac{3400}{3} \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 156 & 0 & -\\frac{220}{3} & 0 & 0 & 0 & \\frac{748000}{3}\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 s1 s2 s3 s4 s5| rhs]\n", "[--------+--------------------------------------------------------------+--------]\n", "[ s1| 0 5/2 1 -5/6 0 0 0| 5000/3]\n", "[ s5| 0 1/5 0 1/3 0 0 1| 1600/3]\n", "[ s3| 0 36/5 0 -14/3 1 0 0| 12400/3]\n", "[ s4| 0 4/5 0 -1/3 0 1 0| 1700/3]\n", "[ x1| 1 1/5 0 1/3 0 0 0| 3400/3]\n", "[--------+--------------------------------------------------------------+--------]\n", "[ Z| 0 156 0 -220/3 0 0 0|748000/3]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "cambio( 3 , 2 )\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 0 & 0 & 1 & \\frac{85}{108} & -\\frac{25}{72} & 0 & 0 & \\frac{6250}{27} \\\\\n", "{\\color{green}{s}}_{5} & 0 & 0 & 0 & \\frac{25}{54} & -\\frac{1}{36} & 0 & 1 & \\frac{11300}{27} \\\\\n", "{x}_{2} & 0 & 1 & 0 & -\\frac{35}{54} & \\frac{5}{36} & 0 & 0 & \\frac{15500}{27} \\\\\n", "{\\color{green}{s}}_{4} & 0 & 0 & 0 & \\frac{5}{27} & -\\frac{1}{9} & 1 & 0 & \\frac{2900}{27} \\\\\n", "{x}_{1} & 1 & 0 & 0 & \\frac{25}{54} & -\\frac{1}{36} & 0 & 0 & \\frac{27500}{27} \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & 0 & \\frac{250}{9} & -\\frac{65}{3} & 0 & 0 & \\frac{3050000}{9}\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 0 & 0 & 1 & \\frac{85}{108} & -\\frac{25}{72} & 0 & 0 & \\frac{6250}{27} \\\\\n", "{\\color{green}{s}}_{5} & 0 & 0 & 0 & \\frac{25}{54} & -\\frac{1}{36} & 0 & 1 & \\frac{11300}{27} \\\\\n", "{x}_{2} & 0 & 1 & 0 & -\\frac{35}{54} & \\frac{5}{36} & 0 & 0 & \\frac{15500}{27} \\\\\n", "{\\color{green}{s}}_{4} & 0 & 0 & 0 & \\frac{5}{27} & -\\frac{1}{9} & 1 & 0 & \\frac{2900}{27} \\\\\n", "{x}_{1} & 1 & 0 & 0 & \\frac{25}{54} & -\\frac{1}{36} & 0 & 0 & \\frac{27500}{27} \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & 0 & \\frac{250}{9} & -\\frac{65}{3} & 0 & 0 & \\frac{3050000}{9}\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 s1 s2 s3 s4 s5| rhs]\n", "[---------+---------------------------------------------------------------------+---------]\n", "[ s1| 0 0 1 85/108 -25/72 0 0| 6250/27]\n", "[ s5| 0 0 0 25/54 -1/36 0 1| 11300/27]\n", "[ x2| 0 1 0 -35/54 5/36 0 0| 15500/27]\n", "[ s4| 0 0 0 5/27 -1/9 1 0| 2900/27]\n", "[ x1| 1 0 0 25/54 -1/36 0 0| 27500/27]\n", "[---------+---------------------------------------------------------------------+---------]\n", "[ Z| 0 0 0 250/9 -65/3 0 0|3050000/9]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "cambio( 1 , 4 )\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{2} & 0 & 0 & \\frac{108}{85} & 1 & -\\frac{15}{34} & 0 & 0 & \\frac{5000}{17} \\\\\n", "{\\color{green}{s}}_{5} & 0 & 0 & -\\frac{10}{17} & 0 & \\frac{3}{17} & 0 & 1 & \\frac{4800}{17} \\\\\n", "{x}_{2} & 0 & 1 & \\frac{14}{17} & 0 & -\\frac{5}{34} & 0 & 0 & \\frac{13000}{17} \\\\\n", "{\\color{green}{s}}_{4} & 0 & 0 & -\\frac{4}{17} & 0 & -\\frac{1}{34} & 1 & 0 & \\frac{900}{17} \\\\\n", "{x}_{1} & 1 & 0 & -\\frac{10}{17} & 0 & \\frac{3}{17} & 0 & 0 & \\frac{15000}{17} \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & -\\frac{600}{17} & 0 & -\\frac{160}{17} & 0 & 0 & \\frac{5900000}{17}\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{2} & 0 & 0 & \\frac{108}{85} & 1 & -\\frac{15}{34} & 0 & 0 & \\frac{5000}{17} \\\\\n", "{\\color{green}{s}}_{5} & 0 & 0 & -\\frac{10}{17} & 0 & \\frac{3}{17} & 0 & 1 & \\frac{4800}{17} \\\\\n", "{x}_{2} & 0 & 1 & \\frac{14}{17} & 0 & -\\frac{5}{34} & 0 & 0 & \\frac{13000}{17} \\\\\n", "{\\color{green}{s}}_{4} & 0 & 0 & -\\frac{4}{17} & 0 & -\\frac{1}{34} & 1 & 0 & \\frac{900}{17} \\\\\n", "{x}_{1} & 1 & 0 & -\\frac{10}{17} & 0 & \\frac{3}{17} & 0 & 0 & \\frac{15000}{17} \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & -\\frac{600}{17} & 0 & -\\frac{160}{17} & 0 & 0 & \\frac{5900000}{17}\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 s1 s2 s3 s4 s5| rhs]\n", "[----------+----------------------------------------------------------------------------+----------]\n", "[ s2| 0 0 108/85 1 -15/34 0 0| 5000/17]\n", "[ s5| 0 0 -10/17 0 3/17 0 1| 4800/17]\n", "[ x2| 0 1 14/17 0 -5/34 0 0| 13000/17]\n", "[ s4| 0 0 -4/17 0 -1/34 1 0| 900/17]\n", "[ x1| 1 0 -10/17 0 3/17 0 0| 15000/17]\n", "[----------+----------------------------------------------------------------------------+----------]\n", "[ Z| 0 0 -600/17 0 -160/17 0 0|5900000/17]" ] }, "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=2 # número de variables x's\n", "m=5 # número de restricciones (distintas de las de signo)\n", "\n", "c=matrix(QQ,1,n,[220,200] ) # vector de costos\n", "\n", "A=matrix(QQ,m,n,[ # coeficientes de las variables x's\n", "[2.5,3],\n", "[3,0.6],\n", "[14,10],\n", "[1,1],\n", "[1,0]\n", "])\n", "\n", "b=matrix(QQ,m,1,[4500,3400,20000,1700,600]) # 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/simplex2023Manual.sage')\n", "#load('https://sage.unex.es/501708/simplex2023AutoREVISED.sage')\n", "#load('https://sage.unex.es/501708/simplex2023CompletamenteManual.sage')\n", "\n" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{rrrrrrr}\n", "\\frac{1}{5} & -\\frac{3}{10} & 0 & -\\frac{3}{10} & -1 & -\\frac{13}{20} & 0 \\\\\n", "0 & \\frac{1}{4} & 0 & -\\frac{1}{4} & 0 & -\\frac{1}{8} & -1 \\\\\n", "-\\frac{3}{5} & \\frac{11}{40} & 1 & -\\frac{19}{40} & 0 & \\frac{61}{80} & 0 \\\\\n", "0 & 0 & 0 & 1 & 0 & 0 & 0 \\\\\n", "\\frac{1}{5} & -\\frac{3}{10} & 0 & -\\frac{3}{10} & 0 & -\\frac{13}{20} & 0 \\\\\n", "0 & 0 & 0 & 0 & 0 & 1 & 0 \\\\\n", "0 & \\frac{1}{4} & 0 & -\\frac{1}{4} & 0 & -\\frac{1}{8} & 0\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{rrrrrrr}\n", "\\frac{1}{5} & -\\frac{3}{10} & 0 & -\\frac{3}{10} & -1 & -\\frac{13}{20} & 0 \\\\\n", "0 & \\frac{1}{4} & 0 & -\\frac{1}{4} & 0 & -\\frac{1}{8} & -1 \\\\\n", "-\\frac{3}{5} & \\frac{11}{40} & 1 & -\\frac{19}{40} & 0 & \\frac{61}{80} & 0 \\\\\n", "0 & 0 & 0 & 1 & 0 & 0 & 0 \\\\\n", "\\frac{1}{5} & -\\frac{3}{10} & 0 & -\\frac{3}{10} & 0 & -\\frac{13}{20} & 0 \\\\\n", "0 & 0 & 0 & 0 & 0 & 1 & 0 \\\\\n", "0 & \\frac{1}{4} & 0 & -\\frac{1}{4} & 0 & -\\frac{1}{8} & 0\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ 1/5 -3/10 0 -3/10 -1 -13/20 0]\n", "[ 0 1/4 0 -1/4 0 -1/8 -1]\n", "[ -3/5 11/40 1 -19/40 0 61/80 0]\n", "[ 0 0 0 1 0 0 0]\n", "[ 1/5 -3/10 0 -3/10 0 -13/20 0]\n", "[ 0 0 0 0 0 1 0]\n", "[ 0 1/4 0 -1/4 0 -1/8 0]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "show(BM1)" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[108/85]\n", "[-10/17]\n", "[ 14/17]\n", "[ -4/17]\n", "[-10/17]" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "bp=matrix(QQ,m,1,[1,0,0,0,0]); BM1*bp " ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrr|rr}\n", "{Basic} & {x}_{1} & {x}_{2} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {b} & {b_1} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{2} & 0 & 0 & \\frac{108}{85} & 1 & -\\frac{15}{34} & 0 & 0 & \\frac{5000}{17} & \\frac{108}{85} \\\\\n", "{\\color{green}{s}}_{5} & 0 & 0 & -\\frac{10}{17} & 0 & \\frac{3}{17} & 0 & 1 & \\frac{4800}{17} & -\\frac{10}{17} \\\\\n", "{x}_{2} & 0 & 1 & \\frac{14}{17} & 0 & -\\frac{5}{34} & 0 & 0 & \\frac{13000}{17} & \\frac{14}{17} \\\\\n", "{\\color{green}{s}}_{4} & 0 & 0 & -\\frac{4}{17} & 0 & -\\frac{1}{34} & 1 & 0 & \\frac{900}{17} & -\\frac{4}{17} \\\\\n", "{x}_{1} & 1 & 0 & -\\frac{10}{17} & 0 & \\frac{3}{17} & 0 & 0 & \\frac{15000}{17} & -\\frac{10}{17} \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & -\\frac{600}{17} & 0 & -\\frac{160}{17} & 0 & 0 & \\frac{5900000}{17} & \\frac{600}{17}\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrr|rr}\n", "{Basic} & {x}_{1} & {x}_{2} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {b} & {b_1} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{2} & 0 & 0 & \\frac{108}{85} & 1 & -\\frac{15}{34} & 0 & 0 & \\frac{5000}{17} & \\frac{108}{85} \\\\\n", "{\\color{green}{s}}_{5} & 0 & 0 & -\\frac{10}{17} & 0 & \\frac{3}{17} & 0 & 1 & \\frac{4800}{17} & -\\frac{10}{17} \\\\\n", "{x}_{2} & 0 & 1 & \\frac{14}{17} & 0 & -\\frac{5}{34} & 0 & 0 & \\frac{13000}{17} & \\frac{14}{17} \\\\\n", "{\\color{green}{s}}_{4} & 0 & 0 & -\\frac{4}{17} & 0 & -\\frac{1}{34} & 1 & 0 & \\frac{900}{17} & -\\frac{4}{17} \\\\\n", "{x}_{1} & 1 & 0 & -\\frac{10}{17} & 0 & \\frac{3}{17} & 0 & 0 & \\frac{15000}{17} & -\\frac{10}{17} \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & -\\frac{600}{17} & 0 & -\\frac{160}{17} & 0 & 0 & \\frac{5900000}{17} & \\frac{600}{17}\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 s1 s2 s3 s4 s5| rhs rhs1]\n", "[----------+----------------------------------------------------------------------------+---------------------]\n", "[ s2| 0 0 108/85 1 -15/34 0 0| 5000/17 108/85]\n", "[ s5| 0 0 -10/17 0 3/17 0 1| 4800/17 -10/17]\n", "[ x2| 0 1 14/17 0 -5/34 0 0| 13000/17 14/17]\n", "[ s4| 0 0 -4/17 0 -1/34 1 0| 900/17 -4/17]\n", "[ x1| 1 0 -10/17 0 3/17 0 0| 15000/17 -10/17]\n", "[----------+----------------------------------------------------------------------------+---------------------]\n", "[ Z| 0 0 -600/17 0 -160/17 0 0|5900000/17 600/17]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "param1b(bp)" ] } ], "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 }