{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"id": "8f1b9136",
"metadata": {
"scrolled": false
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/usr/lib/python3/dist-packages/sage/misc/remote_file.py:46: DeprecationWarning: ssl.SSLContext() without protocol argument is deprecated.\n",
" content = urlopen(req, timeout=1, context=SSLContext())\n",
"/usr/lib/python3/dist-packages/sage/misc/remote_file.py:46: DeprecationWarning: ssl.PROTOCOL_TLS is deprecated\n",
" content = urlopen(req, timeout=1, context=SSLContext())\n"
]
},
{
"data": {
"text/html": [
""
],
"text/latex": [
"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$$"
],
"text/plain": [
"ry"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/html": [
""
],
"text/latex": [
"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$$"
],
"text/plain": [
"ry"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/html": [
""
],
"text/latex": [
"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{l}\n",
"\\begin{array}{lcrcrcrcl}\n",
" \\min \\mspace{-6mu}&\\mspace{-6mu} - \\mspace{-6mu}&\\mspace{-6mu} x_{1} \\mspace{-6mu}&\\mspace{-6mu} - \\mspace{-6mu}&\\mspace{-6mu} 5 x_{2} \\mspace{-6mu}&\\mspace{-6mu} - \\mspace{-6mu}&\\mspace{-6mu} 2 x_{3} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\\\\n",
" \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} x_{1} \\mspace{-6mu}&\\mspace{-6mu} - \\mspace{-6mu}&\\mspace{-6mu} x_{2} \\mspace{-6mu}&\\mspace{-6mu} - \\mspace{-6mu}&\\mspace{-6mu} x_{3} \\mspace{-6mu}&\\mspace{-6mu} \\geq \\mspace{-6mu}&\\mspace{-6mu} 20 \\\\\n",
" \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} x_{2} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 2 x_{3} \\mspace{-6mu}&\\mspace{-6mu} \\geq \\mspace{-6mu}&\\mspace{-6mu} 18 \\\\\n",
"\\end{array} \\\\\n",
"x_{1}, x_{2}, x_{3} \\geq 0\n",
"\\end{array}$$"
],
"text/plain": [
"LP problem (use 'view(...)' or '%display typeset' for details)"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/html": [
""
],
"text/latex": [
"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}-\\infty$$"
],
"text/plain": [
"-Infinity"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/html": [
""
],
"text/latex": [
"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{None}$$"
],
"text/plain": [
"None"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/html": [
""
],
"text/latex": [
"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$$"
],
"text/plain": [
"ry"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/html": [
""
],
"text/latex": [
"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{}$$"
],
"text/plain": [
"salto"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/html": [
""
],
"text/latex": [
"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$$"
],
"text/plain": [
"ry"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/html": [
""
],
"text/latex": [
"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrr|r}\n",
"{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{red}{t}}_{2} & {b} \\\\\n",
"\\hline\n",
" {x}_{1} & 1 & -1 & -1 & -1 & 0 & 0 & 20 \\\\\n",
"{\\color{red}{t}}_{2} & 0 & 1 & 2 & 0 & -1 & 1 & 18 \\\\\n",
"\\hline\n",
" {W_{ind}} & 0 & -1 & -2 & 0 & 1 & 0 & 18\n",
"\\end{array}\\right)$$"
],
"text/plain": [
"[ B| x1 x2 x3 s1 s2 t2|rhs]\n",
"[---+-----------------------+---]\n",
"[ x1| 1 -1 -1 -1 0 0| 20]\n",
"[ t2| 0 1 2 0 -1 1| 18]\n",
"[---+-----------------------+---]\n",
"[ W| 0 -1 -2 0 1 0| 18]"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"tipo='min' # max o min\n",
"\n",
"n=3 # número de variables x's\n",
"m=2 # número de restricciones (distintas de las de signo)\n",
"\n",
"c=matrix(QQ,1,n,[-1,-5,-2] ) # vector de costos\n",
"\n",
"A=matrix(QQ,m,n,[ # coeficientes de las variables x's\n",
"[1,-1,-1],\n",
"[0,1,2]\n",
"])\n",
"\n",
"b=matrix(QQ,m,1,[20,18]) # vector de la derecha\n",
"\n",
"\n",
"######################################################\n",
"############### VARIABLES DE HOLGURA ################\n",
"\n",
"\n",
"h=matrix(ZZ,1,m,[-1,-1]) \n",
"\n",
"t=matrix(ZZ,1,m,[0,1])\n",
"\n",
"colId=(1,6)\n",
"\n",
"\n",
"\n",
"\n",
"\n",
"####################################################################\n",
"############ HASTA AQUÍ LOS DATOS ################################\n",
"####################################################################\n",
"\n",
"\n",
"\n",
"load('https://sage.unex.es/501708/simplex2023CompletamenteManual.sage')\n",
"\n",
"#load('https://sage.unex.es/501708/simplex2023Auto.sage')"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "7ff9f894",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
""
],
"text/latex": [
"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrr|r}\n",
"{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{red}{t}}_{2} & {b} \\\\\n",
"\\hline\n",
" {x}_{1} & 1 & -\\frac{1}{2} & 0 & -1 & -\\frac{1}{2} & \\frac{1}{2} & 29 \\\\\n",
"{x}_{3} & 0 & \\frac{1}{2} & 1 & 0 & -\\frac{1}{2} & \\frac{1}{2} & 9 \\\\\n",
"\\hline\n",
" {W_{ind}} & 0 & 0 & 0 & 0 & 0 & 1 & 0\n",
"\\end{array}\\right)$$"
],
"text/plain": [
"[ B| x1 x2 x3 s1 s2 t2| rhs]\n",
"[----+-----------------------------+----]\n",
"[ x1| 1 -1/2 0 -1 -1/2 1/2| 29]\n",
"[ x3| 0 1/2 1 0 -1/2 1/2| 9]\n",
"[----+-----------------------------+----]\n",
"[ W| 0 0 0 0 0 1| 0]"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"cambio(2,3)"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "88ce80bb",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
""
],
"text/latex": [
"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrr|r}\n",
"{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {b} \\\\\n",
"\\hline\n",
" {x}_{1} & 1 & -\\frac{1}{2} & 0 & -1 & -\\frac{1}{2} & 29 \\\\\n",
"{x}_{3} & 0 & \\frac{1}{2} & 1 & 0 & -\\frac{1}{2} & 9 \\\\\n",
"\\hline\n",
" {Z_{ind}} & 0 & -\\frac{9}{2} & 0 & -1 & -\\frac{3}{2} & -47\n",
"\\end{array}\\right)$$"
],
"text/plain": [
"[ B| x1 x2 x3 s1 s2| rhs]\n",
"[----+------------------------+----]\n",
"[ x1| 1 -1/2 0 -1 -1/2| 29]\n",
"[ x3| 0 1/2 1 0 -1/2| 9]\n",
"[----+------------------------+----]\n",
"[ Z| 0 -9/2 0 -1 -3/2| -47]"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"tt=[0,0];faseII(0,tt)"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "b3cf70a0",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
""
],
"text/latex": [
"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrr|r}\n",
"{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {b} \\\\\n",
"\\hline\n",
" {x}_{1} & 1 & 0 & 1 & -1 & -1 & 38 \\\\\n",
"{x}_{2} & 0 & 1 & 2 & 0 & -1 & 18 \\\\\n",
"\\hline\n",
" {Z_{ind}} & 0 & 0 & 9 & -1 & -6 & -128\n",
"\\end{array}\\right)$$"
],
"text/plain": [
"[ B| x1 x2 x3 s1 s2| rhs]\n",
"[----+------------------------+----]\n",
"[ x1| 1 0 1 -1 -1| 38]\n",
"[ x2| 0 1 2 0 -1| 18]\n",
"[----+------------------------+----]\n",
"[ Z| 0 0 9 -1 -6|-128]"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"cambio(2,2)"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "9684f6ec",
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/usr/lib/python3/dist-packages/sage/misc/remote_file.py:46: DeprecationWarning: ssl.SSLContext() without protocol argument is deprecated.\n",
" content = urlopen(req, timeout=1, context=SSLContext())\n",
"/usr/lib/python3/dist-packages/sage/misc/remote_file.py:46: DeprecationWarning: ssl.PROTOCOL_TLS is deprecated\n",
" content = urlopen(req, timeout=1, context=SSLContext())\n"
]
},
{
"data": {
"text/html": [
""
],
"text/latex": [
"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$$"
],
"text/plain": [
"ry"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/html": [
""
],
"text/latex": [
"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$$"
],
"text/plain": [
"ry"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/html": [
""
],
"text/latex": [
"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{l}\n",
"\\begin{array}{lcrcrcrcl}\n",
" \\min \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} x_{1} \\mspace{-6mu}&\\mspace{-6mu} - \\mspace{-6mu}&\\mspace{-6mu} x_{2} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 2 x_{3} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\\\\n",
" \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} x_{1} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} x_{2} \\mspace{-6mu}&\\mspace{-6mu} - \\mspace{-6mu}&\\mspace{-6mu} x_{3} \\mspace{-6mu}&\\mspace{-6mu} \\geq \\mspace{-6mu}&\\mspace{-6mu} 20 \\\\\n",
" \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} - \\mspace{-6mu}&\\mspace{-6mu} x_{2} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 2 x_{3} \\mspace{-6mu}&\\mspace{-6mu} \\geq \\mspace{-6mu}&\\mspace{-6mu} 18 \\\\\n",
"\\end{array} \\\\\n",
"x_{1}, x_{2}, x_{3} \\geq 0\n",
"\\end{array}$$"
],
"text/plain": [
"LP problem (use 'view(...)' or '%display typeset' for details)"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/html": [
""
],
"text/latex": [
"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}18$$"
],
"text/plain": [
"18"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/html": [
""
],
"text/latex": [
"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(0,\\,58,\\,38\\right)$$"
],
"text/plain": [
"(0, 58, 38)"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/html": [
""
],
"text/latex": [
"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$$"
],
"text/plain": [
"ry"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/html": [
""
],
"text/latex": [
"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{}$$"
],
"text/plain": [
"salto"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/html": [
""
],
"text/latex": [
"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$$"
],
"text/plain": [
"ry"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/html": [
""
],
"text/latex": [
"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrr|r}\n",
"{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{red}{t}}_{2} & {b} \\\\\n",
"\\hline\n",
" {x}_{1} & 1 & 1 & -1 & -1 & 0 & 0 & 20 \\\\\n",
"{\\color{red}{t}}_{2} & 0 & -1 & 2 & 0 & -1 & 1 & 18 \\\\\n",
"\\hline\n",
" {W_{ind}} & 0 & 1 & -2 & 0 & 1 & 0 & 18\n",
"\\end{array}\\right)$$"
],
"text/plain": [
"[ B| x1 x2 x3 s1 s2 t2|rhs]\n",
"[---+-----------------------+---]\n",
"[ x1| 1 1 -1 -1 0 0| 20]\n",
"[ t2| 0 -1 2 0 -1 1| 18]\n",
"[---+-----------------------+---]\n",
"[ W| 0 1 -2 0 1 0| 18]"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"tipo='min' # max o min\n",
"\n",
"n=3 # número de variables x's\n",
"m=2 # número de restricciones (distintas de las de signo)\n",
"\n",
"c=matrix(QQ,1,n,[1,-1,2] ) # vector de costos\n",
"\n",
"A=matrix(QQ,m,n,[ # coeficientes de las variables x's\n",
"[1,1,-1],\n",
"[0,-1,2]\n",
"])\n",
"\n",
"b=matrix(QQ,m,1,[20,18]) # vector de la derecha\n",
"\n",
"\n",
"######################################################\n",
"############### VARIABLES DE HOLGURA ################\n",
"\n",
"\n",
"h=matrix(ZZ,1,m,[-1,-1]) \n",
"t=matrix(ZZ,1,m,[0,1])\n",
"\n",
"colId=(1,6)\n",
"\n",
"\n",
"\n",
"\n",
"\n",
"####################################################################\n",
"############ HASTA AQUÍ LOS DATOS ################################\n",
"####################################################################\n",
"\n",
"\n",
"\n",
"load('https://sage.unex.es/501708/simplex2023CompletamenteManual.sage')\n",
"\n",
"#load('https://sage.unex.es/501708/simplex2023Auto.sage')\n",
"\n",
"\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "1fcb5c41",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
""
],
"text/latex": [
"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrr|r}\n",
"{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{red}{t}}_{2} & {b} \\\\\n",
"\\hline\n",
" {x}_{1} & 1 & \\frac{1}{2} & 0 & -1 & -\\frac{1}{2} & \\frac{1}{2} & 29 \\\\\n",
"{x}_{3} & 0 & -\\frac{1}{2} & 1 & 0 & -\\frac{1}{2} & \\frac{1}{2} & 9 \\\\\n",
"\\hline\n",
" {W_{ind}} & 0 & 0 & 0 & 0 & 0 & 1 & 0\n",
"\\end{array}\\right)$$"
],
"text/plain": [
"[ B| x1 x2 x3 s1 s2 t2| rhs]\n",
"[----+-----------------------------+----]\n",
"[ x1| 1 1/2 0 -1 -1/2 1/2| 29]\n",
"[ x3| 0 -1/2 1 0 -1/2 1/2| 9]\n",
"[----+-----------------------------+----]\n",
"[ W| 0 0 0 0 0 1| 0]"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"cambio(2,3)"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "f1de3171",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
""
],
"text/latex": [
"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrr|r}\n",
"{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {b} \\\\\n",
"\\hline\n",
" {x}_{1} & 1 & \\frac{1}{2} & 0 & -1 & -\\frac{1}{2} & 29 \\\\\n",
"{x}_{3} & 0 & -\\frac{1}{2} & 1 & 0 & -\\frac{1}{2} & 9 \\\\\n",
"\\hline\n",
" {Z_{ind}} & 0 & -\\frac{1}{2} & 0 & 1 & \\frac{3}{2} & 47\n",
"\\end{array}\\right)$$"
],
"text/plain": [
"[ B| x1 x2 x3 s1 s2| rhs]\n",
"[----+------------------------+----]\n",
"[ x1| 1 1/2 0 -1 -1/2| 29]\n",
"[ x3| 0 -1/2 1 0 -1/2| 9]\n",
"[----+------------------------+----]\n",
"[ Z| 0 -1/2 0 1 3/2| 47]"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"tt=[0,0]; faseII(0,tt)"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "77a43c91",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
""
],
"text/latex": [
"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrr|r}\n",
"{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {b} \\\\\n",
"\\hline\n",
" {x}_{2} & 2 & 1 & 0 & -2 & -1 & 58 \\\\\n",
"{x}_{3} & 1 & 0 & 1 & -1 & -1 & 38 \\\\\n",
"\\hline\n",
" {Z_{ind}} & 1 & 0 & 0 & 0 & 1 & 18\n",
"\\end{array}\\right)$$"
],
"text/plain": [
"[ B| x1 x2 x3 s1 s2|rhs]\n",
"[---+-------------------+---]\n",
"[ x2| 2 1 0 -2 -1| 58]\n",
"[ x3| 1 0 1 -1 -1| 38]\n",
"[---+-------------------+---]\n",
"[ Z| 1 0 0 0 1| 18]"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"cambio(1,2)"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "6ccc13d1",
"metadata": {},
"outputs": [],
"source": []
}
],
"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": 5
}