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"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{l}\n",
"\\begin{array}{lcrcrcrcrcrcrcrcl}\n",
" \\min \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} 260 y_{1} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 102 y_{2} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 200 y_{3} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 13 y_{4} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 10 y_{5} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 10 y_{6} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 7 y_{7} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\\\\n",
" \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} 3 y_{1} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} y_{2} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 2 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} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\geq \\mspace{-6mu}&\\mspace{-6mu} 150 \\\\\n",
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" \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} 6 y_{1} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 4 y_{2} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} \\frac{5}{2} 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} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} y_{7} \\mspace{-6mu}&\\mspace{-6mu} \\geq \\mspace{-6mu}&\\mspace{-6mu} 500 \\\\\n",
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"y_{1} \\geq 0,\\ y_{2} \\geq 0,\\ y_{3} \\geq 0,\\ y_{4} \\leq 0,\\ y_{5} \\leq 0,\\ y_{6} \\leq 0,\\ y_{7} \\leq 0\n",
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"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrrrrrr|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} & {\\color{red}{t}}_{4} & {\\color{red}{t}}_{5} & {\\color{red}{t}}_{6} & {\\color{red}{t}}_{7} & {b} \\\\\n",
"\\hline\n",
" {\\color{green}{s}}_{1} & 3 & 5 & 4 & 6 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 260 \\\\\n",
"{\\color{green}{s}}_{2} & 1 & 0 & \\frac{1}{2} & 4 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 102 \\\\\n",
"{\\color{green}{s}}_{3} & 2 & 3 & \\frac{3}{2} & \\frac{5}{2} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 200 \\\\\n",
"{\\color{red}{t}}_{4} & 1 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 13 \\\\\n",
"{\\color{red}{t}}_{5} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 0 & 1 & 0 & 0 & 10 \\\\\n",
"{\\color{red}{t}}_{6} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 0 & 1 & 0 & 10 \\\\\n",
"{\\color{red}{t}}_{7} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 0 & 1 & 7 \\\\\n",
"\\hline\n",
" {W_{ind}} & -1 & -1 & -1 & -1 & 0 & 0 & 0 & 1 & 1 & 1 & 1 & 0 & 0 & 0 & 0 & 40\n",
"\\end{array}\\right)$$"
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"[---+-----------------------------------------------------------+---]\n",
"[ s1| 3 5 4 6 1 0 0 0 0 0 0 0 0 0 0|260]\n",
"[ s2| 1 0 1/2 4 0 1 0 0 0 0 0 0 0 0 0|102]\n",
"[ s3| 2 3 3/2 5/2 0 0 1 0 0 0 0 0 0 0 0|200]\n",
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"[ W| -1 -1 -1 -1 0 0 0 1 1 1 1 0 0 0 0| 40]"
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"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrrrrrr|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} & {\\color{red}{t}}_{4} & {\\color{red}{t}}_{5} & {\\color{red}{t}}_{6} & {\\color{red}{t}}_{7} & {b} \\\\\n",
"\\hline\n",
" {\\color{green}{s}}_{1} & 0 & 5 & 4 & 6 & 1 & 0 & 0 & 3 & 0 & 0 & 0 & -3 & 0 & 0 & 0 & 221 \\\\\n",
"{\\color{green}{s}}_{2} & 0 & 0 & \\frac{1}{2} & 4 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & -1 & 0 & 0 & 0 & 89 \\\\\n",
"{\\color{green}{s}}_{3} & 0 & 3 & \\frac{3}{2} & \\frac{5}{2} & 0 & 0 & 1 & 2 & 0 & 0 & 0 & -2 & 0 & 0 & 0 & 174 \\\\\n",
"{x}_{1} & 1 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 13 \\\\\n",
"{\\color{red}{t}}_{5} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 0 & 1 & 0 & 0 & 10 \\\\\n",
"{\\color{red}{t}}_{6} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 0 & 1 & 0 & 10 \\\\\n",
"{\\color{red}{t}}_{7} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 0 & 1 & 7 \\\\\n",
"\\hline\n",
" {W_{ind}} & 0 & -1 & -1 & -1 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 1 & 0 & 0 & 0 & 27\n",
"\\end{array}\\right)$$"
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"[ s1| 0 5 4 6 1 0 0 3 0 0 0 -3 0 0 0|221]\n",
"[ s2| 0 0 1/2 4 0 1 0 1 0 0 0 -1 0 0 0| 89]\n",
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"[ W| 0 -1 -1 -1 0 0 0 0 1 1 1 1 0 0 0| 27]"
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"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrrrrrr|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} & {\\color{red}{t}}_{4} & {\\color{red}{t}}_{5} & {\\color{red}{t}}_{6} & {\\color{red}{t}}_{7} & {b} \\\\\n",
"\\hline\n",
" {\\color{green}{s}}_{1} & 0 & 0 & 4 & 6 & 1 & 0 & 0 & 3 & 5 & 0 & 0 & -3 & -5 & 0 & 0 & 171 \\\\\n",
"{\\color{green}{s}}_{2} & 0 & 0 & \\frac{1}{2} & 4 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & -1 & 0 & 0 & 0 & 89 \\\\\n",
"{\\color{green}{s}}_{3} & 0 & 0 & \\frac{3}{2} & \\frac{5}{2} & 0 & 0 & 1 & 2 & 3 & 0 & 0 & -2 & -3 & 0 & 0 & 144 \\\\\n",
"{x}_{1} & 1 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 13 \\\\\n",
"{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 0 & 1 & 0 & 0 & 10 \\\\\n",
"{\\color{red}{t}}_{6} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 0 & 1 & 0 & 10 \\\\\n",
"{\\color{red}{t}}_{7} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 0 & 1 & 7 \\\\\n",
"\\hline\n",
" {W_{ind}} & 0 & 0 & -1 & -1 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 1 & 0 & 0 & 17\n",
"\\end{array}\\right)$$"
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"[---+-----------------------------------------------------------+---]\n",
"[ s1| 0 0 4 6 1 0 0 3 5 0 0 -3 -5 0 0|171]\n",
"[ s2| 0 0 1/2 4 0 1 0 1 0 0 0 -1 0 0 0| 89]\n",
"[ s3| 0 0 3/2 5/2 0 0 1 2 3 0 0 -2 -3 0 0|144]\n",
"[ x1| 1 0 0 0 0 0 0 -1 0 0 0 1 0 0 0| 13]\n",
"[ x2| 0 1 0 0 0 0 0 0 -1 0 0 0 1 0 0| 10]\n",
"[ t6| 0 0 1 0 0 0 0 0 0 -1 0 0 0 1 0| 10]\n",
"[ t7| 0 0 0 1 0 0 0 0 0 0 -1 0 0 0 1| 7]\n",
"[---+-----------------------------------------------------------+---]\n",
"[ W| 0 0 -1 -1 0 0 0 0 0 1 1 1 1 0 0| 17]"
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"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrrrrrr|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} & {\\color{red}{t}}_{4} & {\\color{red}{t}}_{5} & {\\color{red}{t}}_{6} & {\\color{red}{t}}_{7} & {b} \\\\\n",
"\\hline\n",
" {\\color{green}{s}}_{1} & 0 & 0 & 0 & 6 & 1 & 0 & 0 & 3 & 5 & 4 & 0 & -3 & -5 & -4 & 0 & 131 \\\\\n",
"{\\color{green}{s}}_{2} & 0 & 0 & 0 & 4 & 0 & 1 & 0 & 1 & 0 & \\frac{1}{2} & 0 & -1 & 0 & -\\frac{1}{2} & 0 & 84 \\\\\n",
"{\\color{green}{s}}_{3} & 0 & 0 & 0 & \\frac{5}{2} & 0 & 0 & 1 & 2 & 3 & \\frac{3}{2} & 0 & -2 & -3 & -\\frac{3}{2} & 0 & 129 \\\\\n",
"{x}_{1} & 1 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 13 \\\\\n",
"{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 0 & 1 & 0 & 0 & 10 \\\\\n",
"{x}_{3} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 0 & 1 & 0 & 10 \\\\\n",
"{\\color{red}{t}}_{7} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 0 & 1 & 7 \\\\\n",
"\\hline\n",
" {W_{ind}} & 0 & 0 & 0 & -1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 1 & 0 & 7\n",
"\\end{array}\\right)$$"
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"[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6 s7 t4 t5 t6 t7| rhs]\n",
"[----+--------------------------------------------------------------------------+----]\n",
"[ s1| 0 0 0 6 1 0 0 3 5 4 0 -3 -5 -4 0| 131]\n",
"[ s2| 0 0 0 4 0 1 0 1 0 1/2 0 -1 0 -1/2 0| 84]\n",
"[ s3| 0 0 0 5/2 0 0 1 2 3 3/2 0 -2 -3 -3/2 0| 129]\n",
"[ x1| 1 0 0 0 0 0 0 -1 0 0 0 1 0 0 0| 13]\n",
"[ x2| 0 1 0 0 0 0 0 0 -1 0 0 0 1 0 0| 10]\n",
"[ x3| 0 0 1 0 0 0 0 0 0 -1 0 0 0 1 0| 10]\n",
"[ t7| 0 0 0 1 0 0 0 0 0 0 -1 0 0 0 1| 7]\n",
"[----+--------------------------------------------------------------------------+----]\n",
"[ W| 0 0 0 -1 0 0 0 0 0 0 1 1 1 1 0| 7]"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"cambio( 7 , 4 )\n"
]
},
{
"data": {
"text/html": [
""
],
"text/latex": [
"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrrrrrr|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} & {\\color{red}{t}}_{4} & {\\color{red}{t}}_{5} & {\\color{red}{t}}_{6} & {\\color{red}{t}}_{7} & {b} \\\\\n",
"\\hline\n",
" {\\color{green}{s}}_{1} & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 3 & 5 & 4 & 6 & -3 & -5 & -4 & -6 & 89 \\\\\n",
"{\\color{green}{s}}_{2} & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 0 & \\frac{1}{2} & 4 & -1 & 0 & -\\frac{1}{2} & -4 & 56 \\\\\n",
"{\\color{green}{s}}_{3} & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 2 & 3 & \\frac{3}{2} & \\frac{5}{2} & -2 & -3 & -\\frac{3}{2} & -\\frac{5}{2} & \\frac{223}{2} \\\\\n",
"{x}_{1} & 1 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 13 \\\\\n",
"{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 0 & 1 & 0 & 0 & 10 \\\\\n",
"{x}_{3} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 0 & 1 & 0 & 10 \\\\\n",
"{x}_{4} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 0 & 1 & 7 \\\\\n",
"\\hline\n",
" {W_{ind}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 1 & 0\n",
"\\end{array}\\right)$$"
],
"text/plain": [
"[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6 s7 t4 t5 t6 t7| rhs]\n",
"[-----+-----------------------------------------------------------------------------------------+-----]\n",
"[ s1| 0 0 0 0 1 0 0 3 5 4 6 -3 -5 -4 -6| 89]\n",
"[ s2| 0 0 0 0 0 1 0 1 0 1/2 4 -1 0 -1/2 -4| 56]\n",
"[ s3| 0 0 0 0 0 0 1 2 3 3/2 5/2 -2 -3 -3/2 -5/2|223/2]\n",
"[ x1| 1 0 0 0 0 0 0 -1 0 0 0 1 0 0 0| 13]\n",
"[ x2| 0 1 0 0 0 0 0 0 -1 0 0 0 1 0 0| 10]\n",
"[ x3| 0 0 1 0 0 0 0 0 0 -1 0 0 0 1 0| 10]\n",
"[ x4| 0 0 0 1 0 0 0 0 0 0 -1 0 0 0 1| 7]\n",
"[-----+-----------------------------------------------------------------------------------------+-----]\n",
"[ W| 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1| 0]"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"El problema de la fase I es óptimo y Wopt=0. Por tanto, el original es factible\n",
"Preparemos el cuadro inicial de la fase II\n"
]
},
{
"data": {
"text/html": [
""
],
"text/latex": [
"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$$"
],
"text/plain": [
"ry"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/html": [
""
],
"text/latex": [
"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{\\ \\ \\ Fase\\ II}$$"
],
"text/plain": [
"FII"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/html": [
""
],
"text/latex": [
"$$\\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|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}}_{1} & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 3 & 5 & 4 & 6 & 89 \\\\\n",
"{\\color{green}{s}}_{2} & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 0 & \\frac{1}{2} & 4 & 56 \\\\\n",
"{\\color{green}{s}}_{3} & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 2 & 3 & \\frac{3}{2} & \\frac{5}{2} & \\frac{223}{2} \\\\\n",
"{x}_{1} & 1 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 0 & 13 \\\\\n",
"{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 10 \\\\\n",
"{x}_{3} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 10 \\\\\n",
"{x}_{4} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 7 \\\\\n",
"\\hline\n",
" {Z_{ind}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 150 & 350 & 250 & 500 & 11450\n",
"\\end{array}\\right)$$"
],
"text/plain": [
"[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6 s7| rhs]\n",
"[-----+-----------------------------------------------------------------+-----]\n",
"[ s1| 0 0 0 0 1 0 0 3 5 4 6| 89]\n",
"[ s2| 0 0 0 0 0 1 0 1 0 1/2 4| 56]\n",
"[ s3| 0 0 0 0 0 0 1 2 3 3/2 5/2|223/2]\n",
"[ x1| 1 0 0 0 0 0 0 -1 0 0 0| 13]\n",
"[ x2| 0 1 0 0 0 0 0 0 -1 0 0| 10]\n",
"[ x3| 0 0 1 0 0 0 0 0 0 -1 0| 10]\n",
"[ x4| 0 0 0 1 0 0 0 0 0 0 -1| 7]\n",
"[-----+-----------------------------------------------------------------+-----]\n",
"[ Z| 0 0 0 0 0 0 0 150 350 250 500|11450]"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"cambio( 2 , 11 )\n"
]
},
{
"data": {
"text/html": [
""
],
"text/latex": [
"$$\\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}}_{1} & 0 & 0 & 0 & 0 & 1 & -\\frac{3}{2} & 0 & \\frac{3}{2} & 5 & \\frac{13}{4} & 0 & 5 \\\\\n",
"{\\color{green}{s}}_{7} & 0 & 0 & 0 & 0 & 0 & \\frac{1}{4} & 0 & \\frac{1}{4} & 0 & \\frac{1}{8} & 1 & 14 \\\\\n",
"{\\color{green}{s}}_{3} & 0 & 0 & 0 & 0 & 0 & -\\frac{5}{8} & 1 & \\frac{11}{8} & 3 & \\frac{19}{16} & 0 & \\frac{153}{2} \\\\\n",
"{x}_{1} & 1 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 0 & 13 \\\\\n",
"{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 10 \\\\\n",
"{x}_{3} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 10 \\\\\n",
"{x}_{4} & 0 & 0 & 0 & 1 & 0 & \\frac{1}{4} & 0 & \\frac{1}{4} & 0 & \\frac{1}{8} & 0 & 21 \\\\\n",
"\\hline\n",
" {Z_{ind}} & 0 & 0 & 0 & 0 & 0 & -125 & 0 & 25 & 350 & \\frac{375}{2} & 0 & 18450\n",
"\\end{array}\\right)$$"
],
"text/plain": [
"[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6 s7| rhs]\n",
"[-----+-----------------------------------------------------------------+-----]\n",
"[ s1| 0 0 0 0 1 -3/2 0 3/2 5 13/4 0| 5]\n",
"[ s7| 0 0 0 0 0 1/4 0 1/4 0 1/8 1| 14]\n",
"[ s3| 0 0 0 0 0 -5/8 1 11/8 3 19/16 0|153/2]\n",
"[ x1| 1 0 0 0 0 0 0 -1 0 0 0| 13]\n",
"[ x2| 0 1 0 0 0 0 0 0 -1 0 0| 10]\n",
"[ x3| 0 0 1 0 0 0 0 0 0 -1 0| 10]\n",
"[ x4| 0 0 0 1 0 1/4 0 1/4 0 1/8 0| 21]\n",
"[-----+-----------------------------------------------------------------+-----]\n",
"[ Z| 0 0 0 0 0 -125 0 25 350 375/2 0|18450]"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"cambio( 1 , 9 )\n"
]
},
{
"data": {
"text/html": [
""
],
"text/latex": [
"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|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}{5} & -\\frac{3}{10} & 0 & \\frac{3}{10} & 1 & \\frac{13}{20} & 0 & 1 \\\\\n",
"{\\color{green}{s}}_{7} & 0 & 0 & 0 & 0 & 0 & \\frac{1}{4} & 0 & \\frac{1}{4} & 0 & \\frac{1}{8} & 1 & 14 \\\\\n",
"{\\color{green}{s}}_{3} & 0 & 0 & 0 & 0 & -\\frac{3}{5} & \\frac{11}{40} & 1 & \\frac{19}{40} & 0 & -\\frac{61}{80} & 0 & \\frac{147}{2} \\\\\n",
"{x}_{1} & 1 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 0 & 13 \\\\\n",
"{x}_{2} & 0 & 1 & 0 & 0 & \\frac{1}{5} & -\\frac{3}{10} & 0 & \\frac{3}{10} & 0 & \\frac{13}{20} & 0 & 11 \\\\\n",
"{x}_{3} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 10 \\\\\n",
"{x}_{4} & 0 & 0 & 0 & 1 & 0 & \\frac{1}{4} & 0 & \\frac{1}{4} & 0 & \\frac{1}{8} & 0 & 21 \\\\\n",
"\\hline\n",
" {Z_{ind}} & 0 & 0 & 0 & 0 & -70 & -20 & 0 & -80 & 0 & -40 & 0 & 18800\n",
"\\end{array}\\right)$$"
],
"text/plain": [
"[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6 s7| rhs]\n",
"[------+----------------------------------------------------------------------------+------]\n",
"[ s5| 0 0 0 0 1/5 -3/10 0 3/10 1 13/20 0| 1]\n",
"[ s7| 0 0 0 0 0 1/4 0 1/4 0 1/8 1| 14]\n",
"[ s3| 0 0 0 0 -3/5 11/40 1 19/40 0 -61/80 0| 147/2]\n",
"[ x1| 1 0 0 0 0 0 0 -1 0 0 0| 13]\n",
"[ x2| 0 1 0 0 1/5 -3/10 0 3/10 0 13/20 0| 11]\n",
"[ x3| 0 0 1 0 0 0 0 0 0 -1 0| 10]\n",
"[ x4| 0 0 0 1 0 1/4 0 1/4 0 1/8 0| 21]\n",
"[------+----------------------------------------------------------------------------+------]\n",
"[ Z| 0 0 0 0 -70 -20 0 -80 0 -40 0| 18800]"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"El problema es óptimo\n"
]
}
],
"source": [
"tipo='max' # max o min\n",
"\n",
"n=4 # número de variables x's\n",
"m=7 # número de restricciones (distintas de las de signo)\n",
"\n",
"c=matrix(QQ,1,n,[150,350,250,500] ) # vector de costos\n",
"\n",
"A=matrix(QQ,m,n,[ # coeficientes de las variables x's\n",
"[3,5,4,6],\n",
"[1,0,0.5,4],\n",
"[2,3,3/2,5/2],\n",
"[1,0,0,0],\n",
"[0,1,0,0],\n",
"[0,0,1,0],\n",
"[0,0,0,1]\n",
"])\n",
"\n",
"b=matrix(QQ,m,1,[260,102,200,13,10,10,7]) # vector de la derecha\n",
"\n",
"\n",
"h=matrix(ZZ,1,m,[1,1,1,-1,-1,-1,-1]) # variables de holgura: \n",
" # Pon 1 si va sumando, \n",
" # -1 si va restando y \n",
" # 0 si no hay variable de holgura.\n",
"#######################################################\n",
"\n",
"\n",
"load('https://sage.unex.es/501708/SAGE/simplex2023Auto.sage')\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
""
],
"text/latex": [
"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrr|rr}\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} & {b_1} \\\\\n",
"\\hline\n",
" {\\color{green}{s}}_{5} & 0 & 0 & 0 & 0 & \\frac{1}{5} & -\\frac{3}{10} & 0 & \\frac{3}{10} & 1 & \\frac{13}{20} & 0 & 1 & 0 \\\\\n",
"{\\color{green}{s}}_{7} & 0 & 0 & 0 & 0 & 0 & \\frac{1}{4} & 0 & \\frac{1}{4} & 0 & \\frac{1}{8} & 1 & 14 & 0 \\\\\n",
"{\\color{green}{s}}_{3} & 0 & 0 & 0 & 0 & -\\frac{3}{5} & \\frac{11}{40} & 1 & \\frac{19}{40} & 0 & -\\frac{61}{80} & 0 & \\frac{147}{2} & 1 \\\\\n",
"{x}_{1} & 1 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 0 & 13 & 0 \\\\\n",
"{x}_{2} & 0 & 1 & 0 & 0 & \\frac{1}{5} & -\\frac{3}{10} & 0 & \\frac{3}{10} & 0 & \\frac{13}{20} & 0 & 11 & 0 \\\\\n",
"{x}_{3} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 10 & 0 \\\\\n",
"{x}_{4} & 0 & 0 & 0 & 1 & 0 & \\frac{1}{4} & 0 & \\frac{1}{4} & 0 & \\frac{1}{8} & 0 & 21 & 0 \\\\\n",
"\\hline\n",
" {Z_{ind}} & 0 & 0 & 0 & 0 & -70 & -20 & 0 & -80 & 0 & -40 & 0 & 18800 & 0\n",
"\\end{array}\\right)$$"
],
"text/plain": [
"[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6 s7| rhs rhs1]\n",
"[------+----------------------------------------------------------------------------+-------------]\n",
"[ s5| 0 0 0 0 1/5 -3/10 0 3/10 1 13/20 0| 1 0]\n",
"[ s7| 0 0 0 0 0 1/4 0 1/4 0 1/8 1| 14 0]\n",
"[ s3| 0 0 0 0 -3/5 11/40 1 19/40 0 -61/80 0| 147/2 1]\n",
"[ x1| 1 0 0 0 0 0 0 -1 0 0 0| 13 0]\n",
"[ x2| 0 1 0 0 1/5 -3/10 0 3/10 0 13/20 0| 11 0]\n",
"[ x3| 0 0 1 0 0 0 0 0 0 -1 0| 10 0]\n",
"[ x4| 0 0 0 1 0 1/4 0 1/4 0 1/8 0| 21 0]\n",
"[------+----------------------------------------------------------------------------+-------------]\n",
"[ Z| 0 0 0 0 -70 -20 0 -80 0 -40 0| 18800 0]"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"b1p=matrix(QQ,m,1,[0,0,1,0,0,0,0]); param1b(b1p)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
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