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"{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {x}_{5} & {b} \\\\\n",
"\\hline\n",
" {x}_{1} & 1 & 0 & 0 & 1 & 2 & 15 \\\\\n",
"{x}_{2} & 0 & 1 & 0 & 2 & 1 & 12 \\\\\n",
"{x}_{3} & 0 & 0 & 1 & 2 & 3 & 0 \\\\\n",
"\\hline\n",
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"[ B| x1 x2 x3 x4 x5|rhs]\n",
"[---+-------------------+---]\n",
"[ x1| 1 0 0 1 2| 15]\n",
"[ x2| 0 1 0 2 1| 12]\n",
"[ x3| 0 0 1 2 3| 0]\n",
"[---+-------------------+---]\n",
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"tipo ='max' # Problema de tipo max o min\n",
"\n",
"n=5 # número de variables x's\n",
"m=3 # número de restricciones (distintas de las de signo)\n",
"\n",
"c=matrix(QQ,1,n,[0,0,0,0,0] ) # vector de costos\n",
"\n",
"A=matrix(QQ,m,n,[ # coeficientes de las variables x's\n",
"[1,0,0,1,2],\n",
"[0,1,0,2,1],\n",
"[0,0,1,2,3]\n",
"])\n",
"\n",
"b=matrix(QQ,m,1,[15,12,0]) # vector de la derecha\n",
"\n",
"\n",
"h=matrix(ZZ,1,m,[0,0,0]) # variables de holgura: \n",
" # Pon 1 si va sumando, \n",
" # -1 si va restando y \n",
" # 0 si no hay variable de holgura.\n",
" \n",
"t=matrix(ZZ,1,m,[0,0,0]) # variables artificiales: \n",
" # pon 1 si utilizas variable artificial en la fila i-ésima\n",
" # 0 si no utilizas variable artificial en la fila i-ésima\n",
"\n",
"colId=(1,2,3) # posición de la matriz identidad\n",
"\n",
"\n",
" \n",
" \n",
"####################################################################\n",
"############ HASTA AQUÍ LOS DATOS ################################\n",
"####################################################################\n",
"\n",
"\n",
"\n",
"\n",
"load('https://sage.unex.es/501708/simplex2023CompletamenteManual.sage')"
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"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrr|r}\n",
"{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {x}_{5} & {b} \\\\\n",
"\\hline\n",
" {x}_{1} & 1 & 0 & -\\frac{1}{2} & 0 & \\frac{1}{2} & 15 \\\\\n",
"{x}_{2} & 0 & 1 & -1 & 0 & -2 & 12 \\\\\n",
"{x}_{4} & 0 & 0 & \\frac{1}{2} & 1 & \\frac{3}{2} & 0 \\\\\n",
"\\hline\n",
" {Z_{ind}} & 0 & 0 & 0 & 0 & 0 & 0\n",
"\\end{array}\\right)$$"
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"[ B| x1 x2 x3 x4 x5| rhs]\n",
"[----+------------------------+----]\n",
"[ x1| 1 0 -1/2 0 1/2| 15]\n",
"[ x2| 0 1 -1 0 -2| 12]\n",
"[ x4| 0 0 1/2 1 3/2| 0]\n",
"[----+------------------------+----]\n",
"[ Z| 0 0 0 0 0| 0]"
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"cambio(3,4)"
]
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"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrr|r}\n",
"{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {x}_{5} & {b} \\\\\n",
"\\hline\n",
" {x}_{1} & 1 & 0 & -\\frac{2}{3} & -\\frac{1}{3} & 0 & 15 \\\\\n",
"{x}_{2} & 0 & 1 & -\\frac{1}{3} & \\frac{4}{3} & 0 & 12 \\\\\n",
"{x}_{5} & 0 & 0 & \\frac{1}{3} & \\frac{2}{3} & 1 & 0 \\\\\n",
"\\hline\n",
" {Z_{ind}} & 0 & 0 & 0 & 0 & 0 & 0\n",
"\\end{array}\\right)$$"
],
"text/plain": [
"[ B| x1 x2 x3 x4 x5| rhs]\n",
"[----+------------------------+----]\n",
"[ x1| 1 0 -2/3 -1/3 0| 15]\n",
"[ x2| 0 1 -1/3 4/3 0| 12]\n",
"[ x5| 0 0 1/3 2/3 1| 0]\n",
"[----+------------------------+----]\n",
"[ Z| 0 0 0 0 0| 0]"
]
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"cambio(3,5)"
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"execution_count": 54,
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"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{l}\n",
"\\begin{array}{lcrcrcrcrcrcl}\n",
" \\max \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} 0 \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\\\\n",
" \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} x_{1} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} x_{4} \\mspace{-6mu}&\\mspace{-6mu} - \\mspace{-6mu}&\\mspace{-6mu} 2 x_{5} \\mspace{-6mu}&\\mspace{-6mu} = \\mspace{-6mu}&\\mspace{-6mu} 5 \\\\\n",
" \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} x_{2} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 2 x_{4} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} x_{5} \\mspace{-6mu}&\\mspace{-6mu} = \\mspace{-6mu}&\\mspace{-6mu} 12 \\\\\n",
" \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} x_{3} \\mspace{-6mu}&\\mspace{-6mu} - \\mspace{-6mu}&\\mspace{-6mu} 2 x_{4} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 3 x_{5} \\mspace{-6mu}&\\mspace{-6mu} = \\mspace{-6mu}&\\mspace{-6mu} 0 \\\\\n",
"\\end{array} \\\\\n",
"x_{1}, x_{2}, x_{3}, x_{4}, x_{5} \\geq 0\n",
"\\end{array}$$"
],
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"LP problem (use 'view(...)' or '%display typeset' for details)"
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"data": {
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""
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""
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"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{}$$"
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""
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"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrr|r}\n",
"{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {x}_{5} & {b} \\\\\n",
"\\hline\n",
" {x}_{1} & 1 & 0 & 0 & 1 & -2 & 5 \\\\\n",
"{x}_{2} & 0 & 1 & 0 & 2 & 1 & 12 \\\\\n",
"{x}_{3} & 0 & 0 & 1 & -2 & 3 & 0 \\\\\n",
"\\hline\n",
" {Z_{ind}} & 0 & 0 & 0 & 0 & 0 & 0\n",
"\\end{array}\\right)$$"
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"[ B| x1 x2 x3 x4 x5|rhs]\n",
"[---+-------------------+---]\n",
"[ x1| 1 0 0 1 -2| 5]\n",
"[ x2| 0 1 0 2 1| 12]\n",
"[ x3| 0 0 1 -2 3| 0]\n",
"[---+-------------------+---]\n",
"[ Z| 0 0 0 0 0| 0]"
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"#https://www.geogebra.org/calculator/zzyxbtjg\n",
"\n",
"#https://www.geogebra.org/calculator/ewdp74gu\n",
"\n",
"tipo ='max' # Problema de tipo max o min\n",
"\n",
"n=5 # número de variables x's\n",
"m=3 # número de restricciones (distintas de las de signo)\n",
"\n",
"c=matrix(QQ,1,n,[0,0,0,0,0] ) # vector de costos\n",
"\n",
"A=matrix(QQ,m,n,[ # coeficientes de las variables x's\n",
"[1,0,0,1,-2],\n",
"[0,1,0,2,1],\n",
"[0,0,1,-2,3]\n",
"])\n",
"\n",
"b=matrix(QQ,m,1,[5,12,0]) # vector de la derecha\n",
"\n",
"\n",
"h=matrix(ZZ,1,m,[0,0,0]) # variables de holgura: \n",
" # Pon 1 si va sumando, \n",
" # -1 si va restando y \n",
" # 0 si no hay variable de holgura.\n",
" \n",
"t=matrix(ZZ,1,m,[0,0,0]) # variables artificiales: \n",
" # pon 1 si utilizas variable artificial en la fila i-ésima\n",
" # 0 si no utilizas variable artificial en la fila i-ésima\n",
"\n",
"colId=(1,2,3) # posición de la matriz identidad\n",
"\n",
"\n",
" \n",
" \n",
"####################################################################\n",
"############ HASTA AQUÍ LOS DATOS ################################\n",
"####################################################################\n",
"\n",
"\n",
"\n",
"\n",
"load('https://sage.unex.es/501708/simplex2023CompletamenteManual.sage')"
]
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"execution_count": 55,
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""
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"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrr|r}\n",
"{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {x}_{5} & {b} \\\\\n",
"\\hline\n",
" {x}_{1} & 1 & -\\frac{1}{2} & 0 & 0 & -\\frac{5}{2} & -1 \\\\\n",
"{x}_{4} & 0 & \\frac{1}{2} & 0 & 1 & \\frac{1}{2} & 6 \\\\\n",
"{x}_{3} & 0 & 1 & 1 & 0 & 4 & 12 \\\\\n",
"\\hline\n",
" {Z_{ind}} & 0 & 0 & 0 & 0 & 0 & 0\n",
"\\end{array}\\right)$$"
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"[ B| x1 x2 x3 x4 x5| rhs]\n",
"[----+------------------------+----]\n",
"[ x1| 1 -1/2 0 0 -5/2| -1]\n",
"[ x4| 0 1/2 0 1 1/2| 6]\n",
"[ x3| 0 1 1 0 4| 12]\n",
"[----+------------------------+----]\n",
"[ Z| 0 0 0 0 0| 0]"
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"cambio(2,4)"
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"\\hline\n",
" {x}_{1} & 1 & \\frac{1}{8} & \\frac{5}{8} & 0 & 0 & \\frac{13}{2} \\\\\n",
"{x}_{4} & 0 & \\frac{3}{8} & -\\frac{1}{8} & 1 & 0 & \\frac{9}{2} \\\\\n",
"{x}_{5} & 0 & \\frac{1}{4} & \\frac{1}{4} & 0 & 1 & 3 \\\\\n",
"\\hline\n",
" {Z_{ind}} & 0 & 0 & 0 & 0 & 0 & 0\n",
"\\end{array}\\right)$$"
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"[ B| x1 x2 x3 x4 x5| rhs]\n",
"[----+------------------------+----]\n",
"[ x1| 1 1/8 5/8 0 0|13/2]\n",
"[ x4| 0 3/8 -1/8 1 0| 9/2]\n",
"[ x5| 0 1/4 1/4 0 1| 3]\n",
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"data": {
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"[ NO]\n",
"[12.000]"
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"source": [
"cocientes(3)"
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"execution_count": 58,
"metadata": {},
"outputs": [],
"source": [
"#cambio(2,2)"
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{
"cell_type": "code",
"execution_count": 59,
"metadata": {},
"outputs": [],
"source": [
"#cambio(3,2)"
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{
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"execution_count": 60,
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"\\hline\n",
" {x}_{3} & \\frac{8}{5} & \\frac{1}{5} & 1 & 0 & 0 & \\frac{52}{5} \\\\\n",
"{x}_{4} & \\frac{1}{5} & \\frac{2}{5} & 0 & 1 & 0 & \\frac{29}{5} \\\\\n",
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