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" content = urlopen(req, timeout=1, context=SSLContext())\n",
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" \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} 8 y_{1} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 6 y_{2} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 5 y_{3} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} y_{4} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\geq \\mspace{-6mu}&\\mspace{-6mu} 1750 \\\\\n",
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"\\end{array} \\\\\n",
"y_{1} \\geq 0,\\ y_{2} \\geq 0,\\ y_{3} \\geq 0,\\ y_{4} \\geq 0,\\ y_{5} \\leq 0,\\ y_{6} \\geq 0\n",
"\\end{array}$$"
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"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{\\ \\ \\ Fase\\ I}$$"
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"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrr|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} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {\\color{red}{t}}_{5} & {b} \\\\\n",
"\\hline\n",
" {\\color{green}{s}}_{1} & 8 & 6 & 3 & 7 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 25001 \\\\\n",
"{\\color{green}{s}}_{2} & 6 & 5 & 2 & 8 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 16867 \\\\\n",
"{\\color{green}{s}}_{3} & 5 & 4 & 2 & 6 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 16669 \\\\\n",
"{\\color{green}{s}}_{4} & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 400 \\\\\n",
"{\\color{red}{t}}_{5} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 1 & 500 \\\\\n",
"{\\color{green}{s}}_{6} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 600 \\\\\n",
"\\hline\n",
" {W_{ind}} & 0 & -1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 500\n",
"\\end{array}\\right)$$"
],
"text/plain": [
"[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6 t5| rhs]\n",
"[-----+-----------------------------------------------------------------+-----]\n",
"[ s1| 8 6 3 7 1 0 0 0 0 0 0|25001]\n",
"[ s2| 6 5 2 8 0 1 0 0 0 0 0|16867]\n",
"[ s3| 5 4 2 6 0 0 1 0 0 0 0|16669]\n",
"[ s4| 1 0 0 0 0 0 0 1 0 0 0| 400]\n",
"[ t5| 0 1 0 0 0 0 0 0 -1 0 1| 500]\n",
"[ s6| 0 0 0 1 0 0 0 0 0 1 0| 600]\n",
"[-----+-----------------------------------------------------------------+-----]\n",
"[ W| 0 -1 0 0 0 0 0 0 1 0 0| 500]"
]
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"text": [
"cambio( 5 , 2 )\n"
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"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrr|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} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {\\color{red}{t}}_{5} & {b} \\\\\n",
"\\hline\n",
" {\\color{green}{s}}_{1} & 8 & 0 & 3 & 7 & 1 & 0 & 0 & 0 & 6 & 0 & -6 & 22001 \\\\\n",
"{\\color{green}{s}}_{2} & 6 & 0 & 2 & 8 & 0 & 1 & 0 & 0 & 5 & 0 & -5 & 14367 \\\\\n",
"{\\color{green}{s}}_{3} & 5 & 0 & 2 & 6 & 0 & 0 & 1 & 0 & 4 & 0 & -4 & 14669 \\\\\n",
"{\\color{green}{s}}_{4} & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 400 \\\\\n",
"{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 1 & 500 \\\\\n",
"{\\color{green}{s}}_{6} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 600 \\\\\n",
"\\hline\n",
" {W_{ind}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0\n",
"\\end{array}\\right)$$"
],
"text/plain": [
"[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6 t5| rhs]\n",
"[-----+-----------------------------------------------------------------+-----]\n",
"[ s1| 8 0 3 7 1 0 0 0 6 0 -6|22001]\n",
"[ s2| 6 0 2 8 0 1 0 0 5 0 -5|14367]\n",
"[ s3| 5 0 2 6 0 0 1 0 4 0 -4|14669]\n",
"[ s4| 1 0 0 0 0 0 0 1 0 0 0| 400]\n",
"[ x2| 0 1 0 0 0 0 0 0 -1 0 1| 500]\n",
"[ s6| 0 0 0 1 0 0 0 0 0 1 0| 600]\n",
"[-----+-----------------------------------------------------------------+-----]\n",
"[ W| 0 0 0 0 0 0 0 0 0 0 1| 0]"
]
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"text": [
"El problema de la fase I es óptimo y Wopt=0. Por tanto, el original es factible\n",
"Preparemos el cuadro inicial de la fase II\n"
]
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"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{\\ \\ \\ Fase\\ II}$$"
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"text/plain": [
"FII"
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"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrr|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} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {b} \\\\\n",
"\\hline\n",
" {\\color{green}{s}}_{1} & 8 & 0 & 3 & 7 & 1 & 0 & 0 & 0 & 6 & 0 & 22001 \\\\\n",
"{\\color{green}{s}}_{2} & 6 & 0 & 2 & 8 & 0 & 1 & 0 & 0 & 5 & 0 & 14367 \\\\\n",
"{\\color{green}{s}}_{3} & 5 & 0 & 2 & 6 & 0 & 0 & 1 & 0 & 4 & 0 & 14669 \\\\\n",
"{\\color{green}{s}}_{4} & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 400 \\\\\n",
"{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 500 \\\\\n",
"{\\color{green}{s}}_{6} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 600 \\\\\n",
"\\hline\n",
" {Z_{ind}} & 1750 & 0 & 900 & 2000 & 0 & 0 & 0 & 0 & 1600 & 0 & 800000\n",
"\\end{array}\\right)$$"
],
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"[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6| rhs]\n",
"[------+---------------------------------------------------------------------+------]\n",
"[ s1| 8 0 3 7 1 0 0 0 6 0| 22001]\n",
"[ s2| 6 0 2 8 0 1 0 0 5 0| 14367]\n",
"[ s3| 5 0 2 6 0 0 1 0 4 0| 14669]\n",
"[ s4| 1 0 0 0 0 0 0 1 0 0| 400]\n",
"[ x2| 0 1 0 0 0 0 0 0 -1 0| 500]\n",
"[ s6| 0 0 0 1 0 0 0 0 0 1| 600]\n",
"[------+---------------------------------------------------------------------+------]\n",
"[ Z| 1750 0 900 2000 0 0 0 0 1600 0|800000]"
]
},
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"text": [
"cambio( 6 , 4 )\n"
]
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"data": {
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"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrr|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} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {b} \\\\\n",
"\\hline\n",
" {\\color{green}{s}}_{1} & 8 & 0 & 3 & 0 & 1 & 0 & 0 & 0 & 6 & -7 & 17801 \\\\\n",
"{\\color{green}{s}}_{2} & 6 & 0 & 2 & 0 & 0 & 1 & 0 & 0 & 5 & -8 & 9567 \\\\\n",
"{\\color{green}{s}}_{3} & 5 & 0 & 2 & 0 & 0 & 0 & 1 & 0 & 4 & -6 & 11069 \\\\\n",
"{\\color{green}{s}}_{4} & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 400 \\\\\n",
"{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 500 \\\\\n",
"{x}_{4} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 600 \\\\\n",
"\\hline\n",
" {Z_{ind}} & 1750 & 0 & 900 & 0 & 0 & 0 & 0 & 0 & 1600 & -2000 & 2000000\n",
"\\end{array}\\right)$$"
],
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"[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6| rhs]\n",
"[-------+-------------------------------------------------------------------------------+-------]\n",
"[ s1| 8 0 3 0 1 0 0 0 6 -7| 17801]\n",
"[ s2| 6 0 2 0 0 1 0 0 5 -8| 9567]\n",
"[ s3| 5 0 2 0 0 0 1 0 4 -6| 11069]\n",
"[ s4| 1 0 0 0 0 0 0 1 0 0| 400]\n",
"[ x2| 0 1 0 0 0 0 0 0 -1 0| 500]\n",
"[ x4| 0 0 0 1 0 0 0 0 0 1| 600]\n",
"[-------+-------------------------------------------------------------------------------+-------]\n",
"[ Z| 1750 0 900 0 0 0 0 0 1600 -2000|2000000]"
]
},
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"text": [
"cambio( 4 , 1 )\n"
]
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"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrr|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} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {b} \\\\\n",
"\\hline\n",
" {\\color{green}{s}}_{1} & 0 & 0 & 3 & 0 & 1 & 0 & 0 & -8 & 6 & -7 & 14601 \\\\\n",
"{\\color{green}{s}}_{2} & 0 & 0 & 2 & 0 & 0 & 1 & 0 & -6 & 5 & -8 & 7167 \\\\\n",
"{\\color{green}{s}}_{3} & 0 & 0 & 2 & 0 & 0 & 0 & 1 & -5 & 4 & -6 & 9069 \\\\\n",
"{x}_{1} & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 400 \\\\\n",
"{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 500 \\\\\n",
"{x}_{4} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 600 \\\\\n",
"\\hline\n",
" {Z_{ind}} & 0 & 0 & 900 & 0 & 0 & 0 & 0 & -1750 & 1600 & -2000 & 2700000\n",
"\\end{array}\\right)$$"
],
"text/plain": [
"[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6| rhs]\n",
"[-------+-------------------------------------------------------------------------------+-------]\n",
"[ s1| 0 0 3 0 1 0 0 -8 6 -7| 14601]\n",
"[ s2| 0 0 2 0 0 1 0 -6 5 -8| 7167]\n",
"[ s3| 0 0 2 0 0 0 1 -5 4 -6| 9069]\n",
"[ x1| 1 0 0 0 0 0 0 1 0 0| 400]\n",
"[ x2| 0 1 0 0 0 0 0 0 -1 0| 500]\n",
"[ x4| 0 0 0 1 0 0 0 0 0 1| 600]\n",
"[-------+-------------------------------------------------------------------------------+-------]\n",
"[ Z| 0 0 900 0 0 0 0 -1750 1600 -2000|2700000]"
]
},
"metadata": {},
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},
{
"name": "stdout",
"output_type": "stream",
"text": [
"cambio( 2 , 9 )\n"
]
},
{
"data": {
"text/html": [
""
],
"text/latex": [
"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrr|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} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {b} \\\\\n",
"\\hline\n",
" {\\color{green}{s}}_{1} & 0 & 0 & \\frac{3}{5} & 0 & 1 & -\\frac{6}{5} & 0 & -\\frac{4}{5} & 0 & \\frac{13}{5} & \\frac{30003}{5} \\\\\n",
"{\\color{green}{s}}_{5} & 0 & 0 & \\frac{2}{5} & 0 & 0 & \\frac{1}{5} & 0 & -\\frac{6}{5} & 1 & -\\frac{8}{5} & \\frac{7167}{5} \\\\\n",
"{\\color{green}{s}}_{3} & 0 & 0 & \\frac{2}{5} & 0 & 0 & -\\frac{4}{5} & 1 & -\\frac{1}{5} & 0 & \\frac{2}{5} & \\frac{16677}{5} \\\\\n",
"{x}_{1} & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 400 \\\\\n",
"{x}_{2} & 0 & 1 & \\frac{2}{5} & 0 & 0 & \\frac{1}{5} & 0 & -\\frac{6}{5} & 0 & -\\frac{8}{5} & \\frac{9667}{5} \\\\\n",
"{x}_{4} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 600 \\\\\n",
"\\hline\n",
" {Z_{ind}} & 0 & 0 & 260 & 0 & 0 & -320 & 0 & 170 & 0 & 560 & 4993440\n",
"\\end{array}\\right)$$"
],
"text/plain": [
"[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6| rhs]\n",
"[-------+-------------------------------------------------------------------------------+-------]\n",
"[ s1| 0 0 3/5 0 1 -6/5 0 -4/5 0 13/5|30003/5]\n",
"[ s5| 0 0 2/5 0 0 1/5 0 -6/5 1 -8/5| 7167/5]\n",
"[ s3| 0 0 2/5 0 0 -4/5 1 -1/5 0 2/5|16677/5]\n",
"[ x1| 1 0 0 0 0 0 0 1 0 0| 400]\n",
"[ x2| 0 1 2/5 0 0 1/5 0 -6/5 0 -8/5| 9667/5]\n",
"[ x4| 0 0 0 1 0 0 0 0 0 1| 600]\n",
"[-------+-------------------------------------------------------------------------------+-------]\n",
"[ Z| 0 0 260 0 0 -320 0 170 0 560|4993440]"
]
},
"metadata": {},
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{
"name": "stdout",
"output_type": "stream",
"text": [
"cambio( 6 , 10 )\n"
]
},
{
"data": {
"text/html": [
""
],
"text/latex": [
"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrr|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} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {b} \\\\\n",
"\\hline\n",
" {\\color{green}{s}}_{1} & 0 & 0 & \\frac{3}{5} & -\\frac{13}{5} & 1 & -\\frac{6}{5} & 0 & -\\frac{4}{5} & 0 & 0 & \\frac{22203}{5} \\\\\n",
"{\\color{green}{s}}_{5} & 0 & 0 & \\frac{2}{5} & \\frac{8}{5} & 0 & \\frac{1}{5} & 0 & -\\frac{6}{5} & 1 & 0 & \\frac{11967}{5} \\\\\n",
"{\\color{green}{s}}_{3} & 0 & 0 & \\frac{2}{5} & -\\frac{2}{5} & 0 & -\\frac{4}{5} & 1 & -\\frac{1}{5} & 0 & 0 & \\frac{15477}{5} \\\\\n",
"{x}_{1} & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 400 \\\\\n",
"{x}_{2} & 0 & 1 & \\frac{2}{5} & \\frac{8}{5} & 0 & \\frac{1}{5} & 0 & -\\frac{6}{5} & 0 & 0 & \\frac{14467}{5} \\\\\n",
"{\\color{green}{s}}_{6} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 600 \\\\\n",
"\\hline\n",
" {Z_{ind}} & 0 & 0 & 260 & -560 & 0 & -320 & 0 & 170 & 0 & 0 & 5329440\n",
"\\end{array}\\right)$$"
],
"text/plain": [
"[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6| rhs]\n",
"[-------+-------------------------------------------------------------------------------+-------]\n",
"[ s1| 0 0 3/5 -13/5 1 -6/5 0 -4/5 0 0|22203/5]\n",
"[ s5| 0 0 2/5 8/5 0 1/5 0 -6/5 1 0|11967/5]\n",
"[ s3| 0 0 2/5 -2/5 0 -4/5 1 -1/5 0 0|15477/5]\n",
"[ x1| 1 0 0 0 0 0 0 1 0 0| 400]\n",
"[ x2| 0 1 2/5 8/5 0 1/5 0 -6/5 0 0|14467/5]\n",
"[ s6| 0 0 0 1 0 0 0 0 0 1| 600]\n",
"[-------+-------------------------------------------------------------------------------+-------]\n",
"[ Z| 0 0 260 -560 0 -320 0 170 0 0|5329440]"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"cambio( 2 , 3 )\n"
]
},
{
"data": {
"text/html": [
""
],
"text/latex": [
"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrr|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} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {b} \\\\\n",
"\\hline\n",
" {\\color{green}{s}}_{1} & 0 & 0 & 0 & -5 & 1 & -\\frac{3}{2} & 0 & 1 & -\\frac{3}{2} & 0 & \\frac{1701}{2} \\\\\n",
"{x}_{3} & 0 & 0 & 1 & 4 & 0 & \\frac{1}{2} & 0 & -3 & \\frac{5}{2} & 0 & \\frac{11967}{2} \\\\\n",
"{\\color{green}{s}}_{3} & 0 & 0 & 0 & -2 & 0 & -1 & 1 & 1 & -1 & 0 & 702 \\\\\n",
"{x}_{1} & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 400 \\\\\n",
"{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 500 \\\\\n",
"{\\color{green}{s}}_{6} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 600 \\\\\n",
"\\hline\n",
" {Z_{ind}} & 0 & 0 & 0 & -1600 & 0 & -450 & 0 & 950 & -650 & 0 & 6885150\n",
"\\end{array}\\right)$$"
],
"text/plain": [
"[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6| rhs]\n",
"[-------+-------------------------------------------------------------------------------+-------]\n",
"[ s1| 0 0 0 -5 1 -3/2 0 1 -3/2 0| 1701/2]\n",
"[ x3| 0 0 1 4 0 1/2 0 -3 5/2 0|11967/2]\n",
"[ s3| 0 0 0 -2 0 -1 1 1 -1 0| 702]\n",
"[ x1| 1 0 0 0 0 0 0 1 0 0| 400]\n",
"[ x2| 0 1 0 0 0 0 0 0 -1 0| 500]\n",
"[ s6| 0 0 0 1 0 0 0 0 0 1| 600]\n",
"[-------+-------------------------------------------------------------------------------+-------]\n",
"[ Z| 0 0 0 -1600 0 -450 0 950 -650 0|6885150]"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"cambio( 4 , 8 )\n"
]
},
{
"data": {
"text/html": [
""
],
"text/latex": [
"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrr|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} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {b} \\\\\n",
"\\hline\n",
" {\\color{green}{s}}_{1} & -1 & 0 & 0 & -5 & 1 & -\\frac{3}{2} & 0 & 0 & -\\frac{3}{2} & 0 & \\frac{901}{2} \\\\\n",
"{x}_{3} & 3 & 0 & 1 & 4 & 0 & \\frac{1}{2} & 0 & 0 & \\frac{5}{2} & 0 & \\frac{14367}{2} \\\\\n",
"{\\color{green}{s}}_{3} & -1 & 0 & 0 & -2 & 0 & -1 & 1 & 0 & -1 & 0 & 302 \\\\\n",
"{\\color{green}{s}}_{4} & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 400 \\\\\n",
"{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 500 \\\\\n",
"{\\color{green}{s}}_{6} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 600 \\\\\n",
"\\hline\n",
" {Z_{ind}} & -950 & 0 & 0 & -1600 & 0 & -450 & 0 & 0 & -650 & 0 & 7265150\n",
"\\end{array}\\right)$$"
],
"text/plain": [
"[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6| rhs]\n",
"[-------+-------------------------------------------------------------------------------+-------]\n",
"[ s1| -1 0 0 -5 1 -3/2 0 0 -3/2 0| 901/2]\n",
"[ x3| 3 0 1 4 0 1/2 0 0 5/2 0|14367/2]\n",
"[ s3| -1 0 0 -2 0 -1 1 0 -1 0| 302]\n",
"[ s4| 1 0 0 0 0 0 0 1 0 0| 400]\n",
"[ x2| 0 1 0 0 0 0 0 0 -1 0| 500]\n",
"[ s6| 0 0 0 1 0 0 0 0 0 1| 600]\n",
"[-------+-------------------------------------------------------------------------------+-------]\n",
"[ Z| -950 0 0 -1600 0 -450 0 0 -650 0|7265150]"
]
},
"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=4 # número de variables x's\n",
"m=6 # número de restricciones (distintas de las de signo)\n",
"\n",
"c=matrix(QQ,1,n,[1750,1600,900,2000] ) # vector de costos\n",
"\n",
"A=matrix(QQ,m,n,[ # coeficientes de las variables x's\n",
"[8,6,3,7],\n",
"[6,5,2,8],\n",
"[5,4,2,6],\n",
"[1,0,0,0],\n",
"[0,1,0,0],\n",
"[0,0,0,1]\n",
"])\n",
"\n",
"b=matrix(QQ,m,1,[25001,16867,16669,400,500,600]) # vector de la derecha\n",
"\n",
"\n",
"######################################################\n",
"############### VARIABLES DE HOLGURA ################\n",
"\n",
"\n",
"h=matrix(ZZ,1,m,[1,1,1,1,-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",
"\n",
"\n",
"####################################################################\n",
"############ HASTA AQUÍ LOS DATOS ################################\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/simplex2023CompletamenteManual.sage')\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"b1p=matrix(QQ,m,1,[1,0,0,0,0,0]); param1b(b1p) "
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"cocientesD(3)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"cambio(3,10)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"tipo='max' # max o min\n",
"\n",
"n=4 # número de variables x's\n",
"m=6 # número de restricciones (distintas de las de signo)\n",
"\n",
"c=matrix(QQ,1,n,[1750,1200,700,2000] ) # vector de costos\n",
"\n",
"A=matrix(QQ,m,n,[ # coeficientes de las variables x's\n",
"[8,6,3,7],\n",
"[6,5,2,8],\n",
"[5,4,2,6],\n",
"[0,1,0,0],\n",
"[0,0,1,0],\n",
"[0,0,0,1]\n",
"])\n",
"\n",
"b=matrix(QQ,m,1,[20000,16000,14000,200,400,500]) # vector de la derecha\n",
"\n",
"\n",
"######################################################\n",
"############### VARIABLES DE HOLGURA ################\n",
"\n",
"\n",
"h=matrix(ZZ,1,m,[1,1,1,-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",
"\n",
"\n",
"####################################################################\n",
"############ HASTA AQUÍ LOS DATOS ################################\n",
"####################################################################\n",
"\n",
"load('https://sage.unex.es/501708/simplex2023Auto.sage')\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"b1p=matrix(QQ,m,1,[0,1,0,0,0,0]); param1b(b1p) "
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"tipo='max' # max o min\n",
"\n",
"n=4 # número de variables x's\n",
"m=6 # número de restricciones (distintas de las de signo)\n",
"\n",
"c=matrix(QQ,1,n,[1750,1200,700,2000] ) # vector de costos\n",
"\n",
"A=matrix(QQ,m,n,[ # coeficientes de las variables x's\n",
"[8,6,3,7],\n",
"[6,5,2,8],\n",
"[5,4,2,6],\n",
"[0,1,0,0],\n",
"[0,0,1,0],\n",
"[0,0,0,1]\n",
"])\n",
"\n",
"b=matrix(QQ,m,1,[20000,16000,14000,200,400,500]) # vector de la derecha\n",
"\n",
"\n",
"######################################################\n",
"############### VARIABLES DE HOLGURA ################\n",
"\n",
"\n",
"h=matrix(ZZ,1,m,[1,1,1,-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",
"\n",
"\n",
"####################################################################\n",
"############ HASTA AQUÍ LOS DATOS ################################\n",
"####################################################################\n",
"\n",
"load('https://sage.unex.es/501708/simplex2023Auto.sage')\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"b1p=matrix(QQ,m,1,[0,0,1,0,0,0]); param1b(b1p) "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Apartado c). Eliminar el compromiso de preoducir 200 unidades del artículo A2."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"tipo='max' # max o min\n",
"\n",
"n=4 # número de variables x's\n",
"m=6 # número de restricciones (distintas de las de signo)\n",
"\n",
"c=matrix(QQ,1,n,[1750,1200,700,2000] ) # vector de costos\n",
"\n",
"A=matrix(QQ,m,n,[ # coeficientes de las variables x's\n",
"[8,6,3,7],\n",
"[6,5,2,8],\n",
"[5,4,2,6],\n",
"[0,1,0,0],\n",
"[0,0,1,0],\n",
"[0,0,0,1]\n",
"])\n",
"\n",
"b=matrix(QQ,m,1,[20000,16000,14000,200,400,500]) # vector de la derecha\n",
"\n",
"\n",
"######################################################\n",
"############### VARIABLES DE HOLGURA ################\n",
"\n",
"\n",
"h=matrix(ZZ,1,m,[1,1,1,-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",
"\n",
"\n",
"####################################################################\n",
"############ HASTA AQUÍ LOS DATOS ################################\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/simplex2023CompletamenteManual.sage'"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"bp=matrix(QQ,m,1,[0,0,0,1,0,0]); param1b(bp)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Apartado e) Añadir $x_1 \\geq 0$"
]
},
{
"cell_type": "code",
"execution_count": 47,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
""
],
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"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$$"
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"text/plain": [
"ry"
]
},
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"output_type": "display_data"
},
{
"data": {
"text/html": [
""
],
"text/latex": [
"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$$"
],
"text/plain": [
"ry"
]
},
"metadata": {},
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},
{
"data": {
"text/html": [
""
],
"text/latex": [
"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{l}\n",
"\\begin{array}{lcrcrcrcrcl}\n",
" \\max \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} 1750 x_{1} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 1200 x_{2} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 700 x_{3} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 2000 x_{4} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\\\\n",
" \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} 8 x_{1} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 6 x_{2} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 3 x_{3} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 7 x_{4} \\mspace{-6mu}&\\mspace{-6mu} \\leq \\mspace{-6mu}&\\mspace{-6mu} 20000 \\\\\n",
" \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} 6 x_{1} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 5 x_{2} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 2 x_{3} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 8 x_{4} \\mspace{-6mu}&\\mspace{-6mu} \\leq \\mspace{-6mu}&\\mspace{-6mu} 16000 \\\\\n",
" \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} 5 x_{1} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 4 x_{2} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 2 x_{3} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 6 x_{4} \\mspace{-6mu}&\\mspace{-6mu} \\leq \\mspace{-6mu}&\\mspace{-6mu} 14000 \\\\\n",
" \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} x_{2} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\geq \\mspace{-6mu}&\\mspace{-6mu} 200 \\\\\n",
" \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} x_{3} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\geq \\mspace{-6mu}&\\mspace{-6mu} 400 \\\\\n",
" \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} x_{4} \\mspace{-6mu}&\\mspace{-6mu} \\leq \\mspace{-6mu}&\\mspace{-6mu} 500 \\\\\n",
"\\end{array} \\\\\n",
"x_{1}, x_{2}, x_{3}, x_{4} \\geq 0\n",
"\\end{array}$$"
],
"text/plain": [
"LP problem (use 'view(...)' or '%display typeset' for details)"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
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""
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"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}4810000$$"
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"4810000"
]
},
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{
"data": {
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""
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"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{l}\n",
"\\begin{array}{lcrcrcrcrcrcrcl}\n",
" \\min \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} 20000 y_{1} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 16000 y_{2} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 14000 y_{3} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 200 y_{4} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 400 y_{5} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 500 y_{6} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\\\\n",
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" \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} 6 y_{1} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 5 y_{2} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 4 y_{3} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} y_{4} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\geq \\mspace{-6mu}&\\mspace{-6mu} 1200 \\\\\n",
" \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} 3 y_{1} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 2 y_{2} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 2 y_{3} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} y_{5} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\geq \\mspace{-6mu}&\\mspace{-6mu} 700 \\\\\n",
" \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} 7 y_{1} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 8 y_{2} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 6 y_{3} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} y_{6} \\mspace{-6mu}&\\mspace{-6mu} \\geq \\mspace{-6mu}&\\mspace{-6mu} 2000 \\\\\n",
"\\end{array} \\\\\n",
"y_{1} \\geq 0,\\ y_{2} \\geq 0,\\ y_{3} \\geq 0,\\ y_{4} \\leq 0,\\ y_{5} \\leq 0,\\ y_{6} \\geq 0\n",
"\\end{array}$$"
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"LP problem (use 'view(...)' or '%display typeset' for details)"
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"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(50,\\,0,\\,275,\\,-200,\\,0,\\,0\\right)$$"
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"text/latex": [
"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{\\ \\ \\ Fase\\ I}$$"
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"text/plain": [
"FI"
]
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"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrrr|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} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {\\color{red}{t}}_{4} & {\\color{red}{t}}_{5} & {b} \\\\\n",
"\\hline\n",
" {\\color{green}{s}}_{1} & 8 & 6 & 3 & 7 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 20000 \\\\\n",
"{\\color{green}{s}}_{2} & 6 & 5 & 2 & 8 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 16000 \\\\\n",
"{\\color{green}{s}}_{3} & 5 & 4 & 2 & 6 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 14000 \\\\\n",
"{\\color{red}{t}}_{4} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 1 & 0 & 200 \\\\\n",
"{\\color{red}{t}}_{5} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 1 & 400 \\\\\n",
"{\\color{green}{s}}_{6} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 500 \\\\\n",
"\\hline\n",
" {W_{ind}} & 0 & -1 & -1 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 600\n",
"\\end{array}\\right)$$"
],
"text/plain": [
"[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6 t4 t5| rhs]\n",
"[-----+-----------------------------------------------------------------------+-----]\n",
"[ s1| 8 6 3 7 1 0 0 0 0 0 0 0|20000]\n",
"[ s2| 6 5 2 8 0 1 0 0 0 0 0 0|16000]\n",
"[ s3| 5 4 2 6 0 0 1 0 0 0 0 0|14000]\n",
"[ t4| 0 1 0 0 0 0 0 -1 0 0 1 0| 200]\n",
"[ t5| 0 0 1 0 0 0 0 0 -1 0 0 1| 400]\n",
"[ s6| 0 0 0 1 0 0 0 0 0 1 0 0| 500]\n",
"[-----+-----------------------------------------------------------------------+-----]\n",
"[ W| 0 -1 -1 0 0 0 0 1 1 0 0 0| 600]"
]
},
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{
"name": "stdout",
"output_type": "stream",
"text": [
"cambio( 4 , 2 )\n"
]
},
{
"data": {
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""
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"text/latex": [
"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrrr|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} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {\\color{red}{t}}_{4} & {\\color{red}{t}}_{5} & {b} \\\\\n",
"\\hline\n",
" {\\color{green}{s}}_{1} & 8 & 0 & 3 & 7 & 1 & 0 & 0 & 6 & 0 & 0 & -6 & 0 & 18800 \\\\\n",
"{\\color{green}{s}}_{2} & 6 & 0 & 2 & 8 & 0 & 1 & 0 & 5 & 0 & 0 & -5 & 0 & 15000 \\\\\n",
"{\\color{green}{s}}_{3} & 5 & 0 & 2 & 6 & 0 & 0 & 1 & 4 & 0 & 0 & -4 & 0 & 13200 \\\\\n",
"{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 1 & 0 & 200 \\\\\n",
"{\\color{red}{t}}_{5} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 1 & 400 \\\\\n",
"{\\color{green}{s}}_{6} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 500 \\\\\n",
"\\hline\n",
" {W_{ind}} & 0 & 0 & -1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 0 & 400\n",
"\\end{array}\\right)$$"
],
"text/plain": [
"[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6 t4 t5| rhs]\n",
"[-----+-----------------------------------------------------------------------+-----]\n",
"[ s1| 8 0 3 7 1 0 0 6 0 0 -6 0|18800]\n",
"[ s2| 6 0 2 8 0 1 0 5 0 0 -5 0|15000]\n",
"[ s3| 5 0 2 6 0 0 1 4 0 0 -4 0|13200]\n",
"[ x2| 0 1 0 0 0 0 0 -1 0 0 1 0| 200]\n",
"[ t5| 0 0 1 0 0 0 0 0 -1 0 0 1| 400]\n",
"[ s6| 0 0 0 1 0 0 0 0 0 1 0 0| 500]\n",
"[-----+-----------------------------------------------------------------------+-----]\n",
"[ W| 0 0 -1 0 0 0 0 0 1 0 1 0| 400]"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"cambio( 5 , 3 )\n"
]
},
{
"data": {
"text/html": [
""
],
"text/latex": [
"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrrr|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} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {\\color{red}{t}}_{4} & {\\color{red}{t}}_{5} & {b} \\\\\n",
"\\hline\n",
" {\\color{green}{s}}_{1} & 8 & 0 & 0 & 7 & 1 & 0 & 0 & 6 & 3 & 0 & -6 & -3 & 17600 \\\\\n",
"{\\color{green}{s}}_{2} & 6 & 0 & 0 & 8 & 0 & 1 & 0 & 5 & 2 & 0 & -5 & -2 & 14200 \\\\\n",
"{\\color{green}{s}}_{3} & 5 & 0 & 0 & 6 & 0 & 0 & 1 & 4 & 2 & 0 & -4 & -2 & 12400 \\\\\n",
"{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 1 & 0 & 200 \\\\\n",
"{x}_{3} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 1 & 400 \\\\\n",
"{\\color{green}{s}}_{6} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 500 \\\\\n",
"\\hline\n",
" {W_{ind}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0\n",
"\\end{array}\\right)$$"
],
"text/plain": [
"[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6 t4 t5| rhs]\n",
"[-----+-----------------------------------------------------------------------+-----]\n",
"[ s1| 8 0 0 7 1 0 0 6 3 0 -6 -3|17600]\n",
"[ s2| 6 0 0 8 0 1 0 5 2 0 -5 -2|14200]\n",
"[ s3| 5 0 0 6 0 0 1 4 2 0 -4 -2|12400]\n",
"[ x2| 0 1 0 0 0 0 0 -1 0 0 1 0| 200]\n",
"[ x3| 0 0 1 0 0 0 0 0 -1 0 0 1| 400]\n",
"[ s6| 0 0 0 1 0 0 0 0 0 1 0 0| 500]\n",
"[-----+-----------------------------------------------------------------------+-----]\n",
"[ W| 0 0 0 0 0 0 0 0 0 0 1 1| 0]"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"El problema de la fase I es óptimo y Wopt=0. Por tanto, el original es factible\n",
"Preparemos el cuadro inicial de la fase II\n"
]
},
{
"data": {
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""
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""
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"text/latex": [
"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{\\ \\ \\ Fase\\ II}$$"
],
"text/plain": [
"FII"
]
},
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{
"data": {
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""
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"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$$"
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""
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"text/latex": [
"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrr|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} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {b} \\\\\n",
"\\hline\n",
" {\\color{green}{s}}_{1} & 8 & 0 & 0 & 7 & 1 & 0 & 0 & 6 & 3 & 0 & 17600 \\\\\n",
"{\\color{green}{s}}_{2} & 6 & 0 & 0 & 8 & 0 & 1 & 0 & 5 & 2 & 0 & 14200 \\\\\n",
"{\\color{green}{s}}_{3} & 5 & 0 & 0 & 6 & 0 & 0 & 1 & 4 & 2 & 0 & 12400 \\\\\n",
"{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 200 \\\\\n",
"{x}_{3} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 400 \\\\\n",
"{\\color{green}{s}}_{6} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 500 \\\\\n",
"\\hline\n",
" {Z_{ind}} & 1750 & 0 & 0 & 2000 & 0 & 0 & 0 & 1200 & 700 & 0 & 520000\n",
"\\end{array}\\right)$$"
],
"text/plain": [
"[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6| rhs]\n",
"[------+---------------------------------------------------------------------+------]\n",
"[ s1| 8 0 0 7 1 0 0 6 3 0| 17600]\n",
"[ s2| 6 0 0 8 0 1 0 5 2 0| 14200]\n",
"[ s3| 5 0 0 6 0 0 1 4 2 0| 12400]\n",
"[ x2| 0 1 0 0 0 0 0 -1 0 0| 200]\n",
"[ x3| 0 0 1 0 0 0 0 0 -1 0| 400]\n",
"[ s6| 0 0 0 1 0 0 0 0 0 1| 500]\n",
"[------+---------------------------------------------------------------------+------]\n",
"[ Z| 1750 0 0 2000 0 0 0 1200 700 0|520000]"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"cambio( 6 , 4 )\n"
]
},
{
"data": {
"text/html": [
""
],
"text/latex": [
"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrr|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} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {b} \\\\\n",
"\\hline\n",
" {\\color{green}{s}}_{1} & 8 & 0 & 0 & 0 & 1 & 0 & 0 & 6 & 3 & -7 & 14100 \\\\\n",
"{\\color{green}{s}}_{2} & 6 & 0 & 0 & 0 & 0 & 1 & 0 & 5 & 2 & -8 & 10200 \\\\\n",
"{\\color{green}{s}}_{3} & 5 & 0 & 0 & 0 & 0 & 0 & 1 & 4 & 2 & -6 & 9400 \\\\\n",
"{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 200 \\\\\n",
"{x}_{3} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 400 \\\\\n",
"{x}_{4} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 500 \\\\\n",
"\\hline\n",
" {Z_{ind}} & 1750 & 0 & 0 & 0 & 0 & 0 & 0 & 1200 & 700 & -2000 & 1520000\n",
"\\end{array}\\right)$$"
],
"text/plain": [
"[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6| rhs]\n",
"[-------+-------------------------------------------------------------------------------+-------]\n",
"[ s1| 8 0 0 0 1 0 0 6 3 -7| 14100]\n",
"[ s2| 6 0 0 0 0 1 0 5 2 -8| 10200]\n",
"[ s3| 5 0 0 0 0 0 1 4 2 -6| 9400]\n",
"[ x2| 0 1 0 0 0 0 0 -1 0 0| 200]\n",
"[ x3| 0 0 1 0 0 0 0 0 -1 0| 400]\n",
"[ x4| 0 0 0 1 0 0 0 0 0 1| 500]\n",
"[-------+-------------------------------------------------------------------------------+-------]\n",
"[ Z| 1750 0 0 0 0 0 0 1200 700 -2000|1520000]"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"cambio( 2 , 1 )\n"
]
},
{
"data": {
"text/html": [
""
],
"text/latex": [
"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrr|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} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {b} \\\\\n",
"\\hline\n",
" {\\color{green}{s}}_{1} & 0 & 0 & 0 & 0 & 1 & -\\frac{4}{3} & 0 & -\\frac{2}{3} & \\frac{1}{3} & \\frac{11}{3} & 500 \\\\\n",
"{x}_{1} & 1 & 0 & 0 & 0 & 0 & \\frac{1}{6} & 0 & \\frac{5}{6} & \\frac{1}{3} & -\\frac{4}{3} & 1700 \\\\\n",
"{\\color{green}{s}}_{3} & 0 & 0 & 0 & 0 & 0 & -\\frac{5}{6} & 1 & -\\frac{1}{6} & \\frac{1}{3} & \\frac{2}{3} & 900 \\\\\n",
"{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 200 \\\\\n",
"{x}_{3} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 400 \\\\\n",
"{x}_{4} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 500 \\\\\n",
"\\hline\n",
" {Z_{ind}} & 0 & 0 & 0 & 0 & 0 & -\\frac{875}{3} & 0 & -\\frac{775}{3} & \\frac{350}{3} & \\frac{1000}{3} & 4495000\n",
"\\end{array}\\right)$$"
],
"text/plain": [
"[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6| rhs]\n",
"[-------+-------------------------------------------------------------------------------+-------]\n",
"[ s1| 0 0 0 0 1 -4/3 0 -2/3 1/3 11/3| 500]\n",
"[ x1| 1 0 0 0 0 1/6 0 5/6 1/3 -4/3| 1700]\n",
"[ s3| 0 0 0 0 0 -5/6 1 -1/6 1/3 2/3| 900]\n",
"[ x2| 0 1 0 0 0 0 0 -1 0 0| 200]\n",
"[ x3| 0 0 1 0 0 0 0 0 -1 0| 400]\n",
"[ x4| 0 0 0 1 0 0 0 0 0 1| 500]\n",
"[-------+-------------------------------------------------------------------------------+-------]\n",
"[ Z| 0 0 0 0 0 -875/3 0 -775/3 350/3 1000/3|4495000]"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"cambio( 1 , 10 )\n"
]
},
{
"data": {
"text/html": [
""
],
"text/latex": [
"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrr|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} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {b} \\\\\n",
"\\hline\n",
" {\\color{green}{s}}_{6} & 0 & 0 & 0 & 0 & \\frac{3}{11} & -\\frac{4}{11} & 0 & -\\frac{2}{11} & \\frac{1}{11} & 1 & \\frac{1500}{11} \\\\\n",
"{x}_{1} & 1 & 0 & 0 & 0 & \\frac{4}{11} & -\\frac{7}{22} & 0 & \\frac{13}{22} & \\frac{5}{11} & 0 & \\frac{20700}{11} \\\\\n",
"{\\color{green}{s}}_{3} & 0 & 0 & 0 & 0 & -\\frac{2}{11} & -\\frac{13}{22} & 1 & -\\frac{1}{22} & \\frac{3}{11} & 0 & \\frac{8900}{11} \\\\\n",
"{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 200 \\\\\n",
"{x}_{3} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 400 \\\\\n",
"{x}_{4} & 0 & 0 & 0 & 1 & -\\frac{3}{11} & \\frac{4}{11} & 0 & \\frac{2}{11} & -\\frac{1}{11} & 0 & \\frac{4000}{11} \\\\\n",
"\\hline\n",
" {Z_{ind}} & 0 & 0 & 0 & 0 & -\\frac{1000}{11} & -\\frac{1875}{11} & 0 & -\\frac{2175}{11} & \\frac{950}{11} & 0 & \\frac{49945000}{11}\n",
"\\end{array}\\right)$$"
],
"text/plain": [
"[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6| rhs]\n",
"[-----------+-----------------------------------------------------------------------------------------------------------------------+-----------]\n",
"[ s6| 0 0 0 0 3/11 -4/11 0 -2/11 1/11 1| 1500/11]\n",
"[ x1| 1 0 0 0 4/11 -7/22 0 13/22 5/11 0| 20700/11]\n",
"[ s3| 0 0 0 0 -2/11 -13/22 1 -1/22 3/11 0| 8900/11]\n",
"[ x2| 0 1 0 0 0 0 0 -1 0 0| 200]\n",
"[ x3| 0 0 1 0 0 0 0 0 -1 0| 400]\n",
"[ x4| 0 0 0 1 -3/11 4/11 0 2/11 -1/11 0| 4000/11]\n",
"[-----------+-----------------------------------------------------------------------------------------------------------------------+-----------]\n",
"[ Z| 0 0 0 0 -1000/11 -1875/11 0 -2175/11 950/11 0|49945000/11]"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"cambio( 1 , 9 )\n"
]
},
{
"data": {
"text/html": [
""
],
"text/latex": [
"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrr|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} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {b} \\\\\n",
"\\hline\n",
" {\\color{green}{s}}_{5} & 0 & 0 & 0 & 0 & 3 & -4 & 0 & -2 & 1 & 11 & 1500 \\\\\n",
"{x}_{1} & 1 & 0 & 0 & 0 & -1 & \\frac{3}{2} & 0 & \\frac{3}{2} & 0 & -5 & 1200 \\\\\n",
"{\\color{green}{s}}_{3} & 0 & 0 & 0 & 0 & -1 & \\frac{1}{2} & 1 & \\frac{1}{2} & 0 & -3 & 400 \\\\\n",
"{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 200 \\\\\n",
"{x}_{3} & 0 & 0 & 1 & 0 & 3 & -4 & 0 & -2 & 0 & 11 & 1900 \\\\\n",
"{x}_{4} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 500 \\\\\n",
"\\hline\n",
" {Z_{ind}} & 0 & 0 & 0 & 0 & -350 & 175 & 0 & -25 & 0 & -950 & 4670000\n",
"\\end{array}\\right)$$"
],
"text/plain": [
"[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6| rhs]\n",
"[-------+-------------------------------------------------------------------------------+-------]\n",
"[ s5| 0 0 0 0 3 -4 0 -2 1 11| 1500]\n",
"[ x1| 1 0 0 0 -1 3/2 0 3/2 0 -5| 1200]\n",
"[ s3| 0 0 0 0 -1 1/2 1 1/2 0 -3| 400]\n",
"[ x2| 0 1 0 0 0 0 0 -1 0 0| 200]\n",
"[ x3| 0 0 1 0 3 -4 0 -2 0 11| 1900]\n",
"[ x4| 0 0 0 1 0 0 0 0 0 1| 500]\n",
"[-------+-------------------------------------------------------------------------------+-------]\n",
"[ Z| 0 0 0 0 -350 175 0 -25 0 -950|4670000]"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"cambio( 2 , 6 )\n"
]
},
{
"data": {
"text/html": [
""
],
"text/latex": [
"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrr|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} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {b} \\\\\n",
"\\hline\n",
" {\\color{green}{s}}_{5} & \\frac{8}{3} & 0 & 0 & 0 & \\frac{1}{3} & 0 & 0 & 2 & 1 & -\\frac{7}{3} & 4700 \\\\\n",
"{\\color{green}{s}}_{2} & \\frac{2}{3} & 0 & 0 & 0 & -\\frac{2}{3} & 1 & 0 & 1 & 0 & -\\frac{10}{3} & 800 \\\\\n",
"{\\color{green}{s}}_{3} & -\\frac{1}{3} & 0 & 0 & 0 & -\\frac{2}{3} & 0 & 1 & 0 & 0 & -\\frac{4}{3} & 0 \\\\\n",
"{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 200 \\\\\n",
"{x}_{3} & \\frac{8}{3} & 0 & 1 & 0 & \\frac{1}{3} & 0 & 0 & 2 & 0 & -\\frac{7}{3} & 5100 \\\\\n",
"{x}_{4} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 500 \\\\\n",
"\\hline\n",
" {Z_{ind}} & -\\frac{350}{3} & 0 & 0 & 0 & -\\frac{700}{3} & 0 & 0 & -200 & 0 & -\\frac{1100}{3} & 4810000\n",
"\\end{array}\\right)$$"
],
"text/plain": [
"[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6| rhs]\n",
"[-------+-------------------------------------------------------------------------------+-------]\n",
"[ s5| 8/3 0 0 0 1/3 0 0 2 1 -7/3| 4700]\n",
"[ s2| 2/3 0 0 0 -2/3 1 0 1 0 -10/3| 800]\n",
"[ s3| -1/3 0 0 0 -2/3 0 1 0 0 -4/3| 0]\n",
"[ x2| 0 1 0 0 0 0 0 -1 0 0| 200]\n",
"[ x3| 8/3 0 1 0 1/3 0 0 2 0 -7/3| 5100]\n",
"[ x4| 0 0 0 1 0 0 0 0 0 1| 500]\n",
"[-------+-------------------------------------------------------------------------------+-------]\n",
"[ Z| -350/3 0 0 0 -700/3 0 0 -200 0 -1100/3|4810000]"
]
},
"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=4 # número de variables x's\n",
"m=6 # número de restricciones (distintas de las de signo)\n",
"\n",
"c=matrix(QQ,1,n,[1750,1200,700,2000] ) # vector de costos\n",
"\n",
"A=matrix(QQ,m,n,[ # coeficientes de las variables x's\n",
"[8,6,3,7],\n",
"[6,5,2,8],\n",
"[5,4,2,6],\n",
"[0,1,0,0],\n",
"[0,0,1,0],\n",
"[0,0,0,1]\n",
"])\n",
"\n",
"b=matrix(QQ,m,1,[20000,16000,14000,200,400,500]) # vector de la derecha\n",
"\n",
"\n",
"######################################################\n",
"############### VARIABLES DE HOLGURA ################\n",
"\n",
"\n",
"h=matrix(ZZ,1,m,[1,1,1,-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",
"\n",
"\n",
"####################################################################\n",
"############ HASTA AQUÍ LOS DATOS ################################\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/simplex2023CompletamenteManual.sage'"
]
},
{
"cell_type": "code",
"execution_count": 48,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"10"
]
},
"execution_count": 48,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"nv"
]
},
{
"cell_type": "code",
"execution_count": 49,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
""
],
"text/latex": [
"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrr|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} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {\\color{green}{s}}_{7} & {b} \\\\\n",
"\\hline\n",
" {\\color{green}{s}}_{5} & \\frac{8}{3} & 0 & 0 & 0 & \\frac{1}{3} & 0 & 0 & 2 & 1 & -\\frac{7}{3} & 0 & 4700 \\\\\n",
"{\\color{green}{s}}_{2} & \\frac{2}{3} & 0 & 0 & 0 & -\\frac{2}{3} & 1 & 0 & 1 & 0 & -\\frac{10}{3} & 0 & 800 \\\\\n",
"{\\color{green}{s}}_{3} & -\\frac{1}{3} & 0 & 0 & 0 & -\\frac{2}{3} & 0 & 1 & 0 & 0 & -\\frac{4}{3} & 0 & 0 \\\\\n",
"{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 0 & 200 \\\\\n",
"{x}_{3} & \\frac{8}{3} & 0 & 1 & 0 & \\frac{1}{3} & 0 & 0 & 2 & 0 & -\\frac{7}{3} & 0 & 5100 \\\\\n",
"{x}_{4} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 500 \\\\\n",
"{\\color{green}{s}}_{7} & -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & -100 \\\\\n",
"\\hline\n",
" {Z_{ind}} & -\\frac{350}{3} & 0 & 0 & 0 & -\\frac{700}{3} & 0 & 0 & -200 & 0 & -\\frac{1100}{3} & 0 & 4810000\n",
"\\end{array}\\right)$$"
],
"text/plain": [
"[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6 s7| rhs]\n",
"[-------+---------------------------------------------------------------------------------------+-------]\n",
"[ s5| 8/3 0 0 0 1/3 0 0 2 1 -7/3 0| 4700]\n",
"[ s2| 2/3 0 0 0 -2/3 1 0 1 0 -10/3 0| 800]\n",
"[ s3| -1/3 0 0 0 -2/3 0 1 0 0 -4/3 0| 0]\n",
"[ x2| 0 1 0 0 0 0 0 -1 0 0 0| 200]\n",
"[ x3| 8/3 0 1 0 1/3 0 0 2 0 -7/3 0| 5100]\n",
"[ x4| 0 0 0 1 0 0 0 0 0 1 0| 500]\n",
"[ s7| -1 0 0 0 0 0 0 0 0 0 1| -100]\n",
"[-------+---------------------------------------------------------------------------------------+-------]\n",
"[ Z| -350/3 0 0 0 -700/3 0 0 -200 0 -1100/3 0|4810000]"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"v=matrix(QQ,1,nv,[-1,0,0,0,0,0,0,0,0,0] ); R=-100;\n",
"añadeRes(v,R)"
]
},
{
"cell_type": "code",
"execution_count": 50,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
""
],
"text/latex": [
"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrr|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} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {\\color{green}{s}}_{7} & {b} \\\\\n",
"\\hline\n",
" {\\color{green}{s}}_{5} & 0 & 0 & 0 & 0 & \\frac{1}{3} & 0 & 0 & 2 & 1 & -\\frac{7}{3} & \\frac{8}{3} & \\frac{13300}{3} \\\\\n",
"{\\color{green}{s}}_{2} & 0 & 0 & 0 & 0 & -\\frac{2}{3} & 1 & 0 & 1 & 0 & -\\frac{10}{3} & \\frac{2}{3} & \\frac{2200}{3} \\\\\n",
"{\\color{green}{s}}_{3} & 0 & 0 & 0 & 0 & -\\frac{2}{3} & 0 & 1 & 0 & 0 & -\\frac{4}{3} & -\\frac{1}{3} & \\frac{100}{3} \\\\\n",
"{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 0 & 200 \\\\\n",
"{x}_{3} & 0 & 0 & 1 & 0 & \\frac{1}{3} & 0 & 0 & 2 & 0 & -\\frac{7}{3} & \\frac{8}{3} & \\frac{14500}{3} \\\\\n",
"{x}_{4} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 500 \\\\\n",
"{x}_{1} & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 100 \\\\\n",
"\\hline\n",
" {Z_{ind}} & 0 & 0 & 0 & 0 & -\\frac{700}{3} & 0 & 0 & -200 & 0 & -\\frac{1100}{3} & -\\frac{350}{3} & \\frac{14395000}{3}\n",
"\\end{array}\\right)$$"
],
"text/plain": [
"[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6 s7| rhs]\n",
"[----------+------------------------------------------------------------------------------------------------------------------------+----------]\n",
"[ s5| 0 0 0 0 1/3 0 0 2 1 -7/3 8/3| 13300/3]\n",
"[ s2| 0 0 0 0 -2/3 1 0 1 0 -10/3 2/3| 2200/3]\n",
"[ s3| 0 0 0 0 -2/3 0 1 0 0 -4/3 -1/3| 100/3]\n",
"[ x2| 0 1 0 0 0 0 0 -1 0 0 0| 200]\n",
"[ x3| 0 0 1 0 1/3 0 0 2 0 -7/3 8/3| 14500/3]\n",
"[ x4| 0 0 0 1 0 0 0 0 0 1 0| 500]\n",
"[ x1| 1 0 0 0 0 0 0 0 0 0 -1| 100]\n",
"[----------+------------------------------------------------------------------------------------------------------------------------+----------]\n",
"[ Z| 0 0 0 0 -700/3 0 0 -200 0 -1100/3 -350/3|14395000/3]"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"cambio(7,1)"
]
}
],
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