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"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrr|r}\n",
"{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{red}{t}}_{1} & {\\color{red}{t}}_{2} & {b} \\\\\n",
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" {\\color{red}{t}}_{1} & -1 & 1 & -1 & 1 & -1 & 0 & 1 & 0 & 6 \\\\\n",
"{\\color{red}{t}}_{2} & -1 & -2 & 2 & -3 & 0 & -1 & 0 & 1 & 4 \\\\\n",
"\\hline\n",
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"\\end{array}\\right)$$"
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"[ B| x1 x2 x3 x4 s1 s2 t1 t2|rhs]\n",
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"[ t1| -1 1 -1 1 -1 0 1 0| 6]\n",
"[ t2| -1 -2 2 -3 0 -1 0 1| 4]\n",
"[---+-------------------------------+---]\n",
"[ W| 2 1 -1 2 1 1 0 0| 10]"
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"tipo='min' # max o min\n",
"\n",
"n=4 # número de variables x's\n",
"m=2 # número de restricciones (distintas de las de signo)\n",
"\n",
"c=matrix(QQ,1,n,[1,2,-2,-3] ) # vector de costos\n",
"\n",
"A=matrix(QQ,m,n,[ # coeficientes de las variables x's\n",
"[-1,1,-1,1],\n",
"[-1,-2,2,-3]\n",
"])\n",
"\n",
"b=matrix(QQ,m,1,[6,4]) # vector de la derecha\n",
"\n",
"\n",
"######################################################\n",
"############### VARIABLES DE HOLGURA ################\n",
"\n",
"\n",
"h=matrix(ZZ,1,m,[-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",
"t=matrix(ZZ,1,m,[1,1])\n",
"\n",
"colId=(7,8)\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')"
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"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrr|r}\n",
"{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{red}{t}}_{1} & {\\color{red}{t}}_{2} & {b} \\\\\n",
"\\hline\n",
" {\\color{red}{t}}_{1} & -\\frac{3}{2} & 0 & 0 & -\\frac{1}{2} & -1 & -\\frac{1}{2} & 1 & \\frac{1}{2} & 8 \\\\\n",
"{x}_{3} & -\\frac{1}{2} & -1 & 1 & -\\frac{3}{2} & 0 & -\\frac{1}{2} & 0 & \\frac{1}{2} & 2 \\\\\n",
"\\hline\n",
" {W_{ind}} & \\frac{3}{2} & 0 & 0 & \\frac{1}{2} & 1 & \\frac{1}{2} & 0 & \\frac{1}{2} & 8\n",
"\\end{array}\\right)$$"
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"[ B| x1 x2 x3 x4 s1 s2 t1 t2| rhs]\n",
"[----+---------------------------------------+----]\n",
"[ t1|-3/2 0 0 -1/2 -1 -1/2 1 1/2| 8]\n",
"[ x3|-1/2 -1 1 -3/2 0 -1/2 0 1/2| 2]\n",
"[----+---------------------------------------+----]\n",
"[ W| 3/2 0 0 1/2 1 1/2 0 1/2| 8]"
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"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{l}\n",
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" \\min \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} - \\mspace{-6mu}&\\mspace{-6mu} 2 x_{2} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} x_{3} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\\\\n",
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"\\end{array} \\\\\n",
"x_{1}, x_{2}, x_{3} \\geq 0\n",
"\\end{array}$$"
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"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrr|r}\n",
"{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{red}{t}}_{1} & {\\color{red}{t}}_{2} & {b} \\\\\n",
"\\hline\n",
" {\\color{red}{t}}_{1} & 1 & -1 & -1 & -1 & 0 & 1 & 0 & 16 \\\\\n",
"{\\color{red}{t}}_{2} & -1 & -1 & 2 & 0 & -1 & 0 & 1 & 12 \\\\\n",
"\\hline\n",
" {W_{ind}} & 0 & 2 & -1 & 1 & 1 & 0 & 0 & 28\n",
"\\end{array}\\right)$$"
],
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"[ B| x1 x2 x3 s1 s2 t1 t2|rhs]\n",
"[---+---------------------------+---]\n",
"[ t1| 1 -1 -1 -1 0 1 0| 16]\n",
"[ t2| -1 -1 2 0 -1 0 1| 12]\n",
"[---+---------------------------+---]\n",
"[ W| 0 2 -1 1 1 0 0| 28]"
]
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"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,[0,-2,1] ) # vector de costos\n",
"\n",
"A=matrix(QQ,m,n,[ # coeficientes de las variables x's\n",
"[1,-1,-1],\n",
"[-1,-1,2]\n",
"])\n",
"\n",
"b=matrix(QQ,m,1,[16,12]) # vector de la derecha\n",
"\n",
"\n",
"######################################################\n",
"############### VARIABLES DE HOLGURA ################\n",
"\n",
"\n",
"h=matrix(ZZ,1,m,[-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",
"t=matrix(ZZ,1,m,[1,1])\n",
"\n",
"colId=(6,7)\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')"
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"execution_count": 18,
"id": "60abcb8c",
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"data": {
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""
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"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrr|r}\n",
"{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{red}{t}}_{1} & {\\color{red}{t}}_{2} & {b} \\\\\n",
"\\hline\n",
" {\\color{red}{t}}_{1} & \\frac{1}{2} & -\\frac{3}{2} & 0 & -1 & -\\frac{1}{2} & 1 & \\frac{1}{2} & 22 \\\\\n",
"{x}_{3} & -\\frac{1}{2} & -\\frac{1}{2} & 1 & 0 & -\\frac{1}{2} & 0 & \\frac{1}{2} & 6 \\\\\n",
"\\hline\n",
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"[ B| x1 x2 x3 s1 s2 t1 t2| rhs]\n",
"[----+----------------------------------+----]\n",
"[ t1| 1/2 -3/2 0 -1 -1/2 1 1/2| 22]\n",
"[ x3|-1/2 -1/2 1 0 -1/2 0 1/2| 6]\n",
"[----+----------------------------------+----]\n",
"[ W|-1/2 3/2 0 1 1/2 0 1/2| 22]"
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"id": "3a704572",
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"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrr|r}\n",
"{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{red}{t}}_{1} & {\\color{red}{t}}_{2} & {b} \\\\\n",
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" {x}_{1} & 1 & -3 & 0 & -2 & -1 & 2 & 1 & 44 \\\\\n",
"{x}_{3} & 0 & -2 & 1 & -1 & -1 & 1 & 1 & 28 \\\\\n",
"\\hline\n",
" {W_{ind}} & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0\n",
"\\end{array}\\right)$$"
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"[ B| x1 x2 x3 s1 s2 t1 t2|rhs]\n",
"[---+---------------------------+---]\n",
"[ x1| 1 -3 0 -2 -1 2 1| 44]\n",
"[ x3| 0 -2 1 -1 -1 1 1| 28]\n",
"[---+---------------------------+---]\n",
"[ W| 0 0 0 0 0 1 1| 0]"
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"$$\\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 & -3 & 0 & -2 & -1 & 44 \\\\\n",
"{x}_{3} & 0 & -2 & 1 & -1 & -1 & 28 \\\\\n",
"\\hline\n",
" {Z_{ind}} & 0 & 0 & 0 & 1 & 1 & 28\n",
"\\end{array}\\right)$$"
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"[ B| x1 x2 x3 s1 s2|rhs]\n",
"[---+-------------------+---]\n",
"[ x1| 1 -3 0 -2 -1| 44]\n",
"[ x3| 0 -2 1 -1 -1| 28]\n",
"[---+-------------------+---]\n",
"[ Z| 0 0 0 1 1| 28]"
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"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{l}\n",
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" \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} 2 x_{1} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 3 x_{2} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 4 x_{3} \\mspace{-6mu}&\\mspace{-6mu} = \\mspace{-6mu}&\\mspace{-6mu} 9 \\\\\n",
" \\mspace{-6mu}&\\mspace{-6mu} - \\mspace{-6mu}&\\mspace{-6mu} x_{1} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 2 x_{2} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 3 x_{3} \\mspace{-6mu}&\\mspace{-6mu} = \\mspace{-6mu}&\\mspace{-6mu} 4 \\\\\n",
"\\end{array} \\\\\n",
"x_{1}, x_{2}, x_{3} \\geq 0\n",
"\\end{array}$$"
],
"text/plain": [
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"data": {
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"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\frac{6}{7},\\,\\frac{17}{7},\\,0\\right)$$"
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"text/latex": [
"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrr|r}\n",
"{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {\\color{red}{t}}_{1} & {\\color{red}{t}}_{2} & {b} \\\\\n",
"\\hline\n",
" {\\color{red}{t}}_{1} & 2 & 3 & 4 & 1 & 0 & 9 \\\\\n",
"{\\color{red}{t}}_{2} & -1 & 2 & 3 & 0 & 1 & 4 \\\\\n",
"\\hline\n",
" {W_{ind}} & -1 & -5 & -7 & 0 & 0 & 13\n",
"\\end{array}\\right)$$"
],
"text/plain": [
"[ B| x1 x2 x3 t1 t2|rhs]\n",
"[---+-------------------+---]\n",
"[ t1| 2 3 4 1 0| 9]\n",
"[ t2| -1 2 3 0 1| 4]\n",
"[---+-------------------+---]\n",
"[ W| -1 -5 -7 0 0| 13]"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"tipo='min' # max o min\n",
"\n",
"n=3 # número de variables x's\n",
"m=2 # número de restricciones (distintas de las de signo)\n",
"\n",
"c=matrix(QQ,1,n,[0,0,0] ) # vector de costos\n",
"\n",
"A=matrix(QQ,m,n,[ # coeficientes de las variables x's\n",
"[2,3,4],\n",
"[-1,2,3]\n",
"])\n",
"\n",
"b=matrix(QQ,m,1,[9,4]) # vector de la derecha\n",
"\n",
"\n",
"######################################################\n",
"############### VARIABLES DE HOLGURA ################\n",
"\n",
"\n",
"h=matrix(ZZ,1,m,[0,0]) # variables de holgura: \n",
" # Pon 1 si va sumando, \n",
" # -1 si va restando y \n",
" # 0 si no hay variable de holgura.\n",
"t=matrix(ZZ,1,m,[1,1])\n",
"\n",
"colId=(4,5)\n",
"\n",
"\n",
"\n",
"\n",
"\n",
"####################################################################\n",
"############ HASTA AQUÍ LOS DATOS ################################\n",
"####################################################################\n",
"\n",
"\n",
"\n",
"load('https://sage.unex.es/501708/simplex2023CompletamenteManual.sage')\n",
"\n",
"#load('https://sage.unex.es/501708/simplex2023Auto.sage')"
]
},
{
"cell_type": "code",
"execution_count": 22,
"id": "8bc5cd32",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
""
],
"text/latex": [
"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrr|r}\n",
"{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {\\color{red}{t}}_{1} & {\\color{red}{t}}_{2} & {b} \\\\\n",
"\\hline\n",
" {\\color{red}{t}}_{1} & \\frac{10}{3} & \\frac{1}{3} & 0 & 1 & -\\frac{4}{3} & \\frac{11}{3} \\\\\n",
"{x}_{3} & -\\frac{1}{3} & \\frac{2}{3} & 1 & 0 & \\frac{1}{3} & \\frac{4}{3} \\\\\n",
"\\hline\n",
" {W_{ind}} & -\\frac{10}{3} & -\\frac{1}{3} & 0 & 0 & \\frac{7}{3} & \\frac{11}{3}\n",
"\\end{array}\\right)$$"
],
"text/plain": [
"[ B| x1 x2 x3 t1 t2| rhs]\n",
"[-----+-----------------------------+-----]\n",
"[ t1| 10/3 1/3 0 1 -4/3| 11/3]\n",
"[ x3| -1/3 2/3 1 0 1/3| 4/3]\n",
"[-----+-----------------------------+-----]\n",
"[ W|-10/3 -1/3 0 0 7/3| 11/3]"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"cambio(2,3)"
]
},
{
"cell_type": "code",
"execution_count": 23,
"id": "6af8ac5d",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
""
],
"text/latex": [
"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrr|r}\n",
"{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {\\color{red}{t}}_{1} & {\\color{red}{t}}_{2} & {b} \\\\\n",
"\\hline\n",
" {x}_{1} & 1 & \\frac{1}{10} & 0 & \\frac{3}{10} & -\\frac{2}{5} & \\frac{11}{10} \\\\\n",
"{x}_{3} & 0 & \\frac{7}{10} & 1 & \\frac{1}{10} & \\frac{1}{5} & \\frac{17}{10} \\\\\n",
"\\hline\n",
" {W_{ind}} & 0 & 0 & 0 & 1 & 1 & 0\n",
"\\end{array}\\right)$$"
],
"text/plain": [
"[ B| x1 x2 x3 t1 t2| rhs]\n",
"[-----+-----------------------------+-----]\n",
"[ x1| 1 1/10 0 3/10 -2/5|11/10]\n",
"[ x3| 0 7/10 1 1/10 1/5|17/10]\n",
"[-----+-----------------------------+-----]\n",
"[ W| 0 0 0 1 1| 0]"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"cambio(1,1)"
]
},
{
"cell_type": "code",
"execution_count": 24,
"id": "ebbd22ef",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
""
],
"text/latex": [
"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrr|r}\n",
"{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {b} \\\\\n",
"\\hline\n",
" {x}_{1} & 1 & \\frac{1}{10} & 0 & \\frac{11}{10} \\\\\n",
"{x}_{3} & 0 & \\frac{7}{10} & 1 & \\frac{17}{10} \\\\\n",
"\\hline\n",
" {Z_{ind}} & 0 & 0 & 0 & 0\n",
"\\end{array}\\right)$$"
],
"text/plain": [
"[ B| x1 x2 x3| rhs]\n",
"[-----+-----------------+-----]\n",
"[ x1| 1 1/10 0|11/10]\n",
"[ x3| 0 7/10 1|17/10]\n",
"[-----+-----------------+-----]\n",
"[ Z| 0 0 0| 0]"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"tt=[0,0];faseII(0,tt)"
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "03730316",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
""
],
"text/latex": [
"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrr|r}\n",
"{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {b} \\\\\n",
"\\hline\n",
" {x}_{1} & 1 & 0 & -\\frac{1}{7} & \\frac{19}{7} \\\\\n",
"{x}_{2} & 0 & 1 & \\frac{10}{7} & \\frac{27}{7} \\\\\n",
"\\hline\n",
" {Z_{ind}} & 0 & 0 & 0 & 0\n",
"\\end{array}\\right)$$"
],
"text/plain": [
"[ B| x1 x2 x3| rhs]\n",
"[----+--------------+----]\n",
"[ x1| 1 0 -1/7|19/7]\n",
"[ x2| 0 1 10/7|27/7]\n",
"[----+--------------+----]\n",
"[ Z| 0 0 0| 0]"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"cambio(2,2)"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "SageMath 9.5",
"language": "sage",
"name": "sagemath"
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"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
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"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
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