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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} 3 x_{1} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 3 x_{2} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 3 x_{3} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} x_{4} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 5 x_{5} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 2 x_{6} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\\\\n",
" \\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} 2 x_{4} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 4 x_{5} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\leq \\mspace{-6mu}&\\mspace{-6mu} 10 \\\\\n",
" \\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} \\mspace{-6mu}&\\mspace{-6mu} - \\mspace{-6mu}&\\mspace{-6mu} x_{4} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 5 x_{5} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} = \\mspace{-6mu}&\\mspace{-6mu} 15 \\\\\n",
" \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} 3 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} 4 x_{5} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} x_{6} \\mspace{-6mu}&\\mspace{-6mu} \\geq \\mspace{-6mu}&\\mspace{-6mu} 25 \\\\\n",
"\\end{array} \\\\\n",
"x_{1}, x_{2}, x_{3}, x_{4}, x_{5}, x_{6} \\geq 0\n",
"\\end{array}$$"
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"(0, 1, 0, 0, 2, 14)"
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"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrr|r}\n",
"{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {x}_{5} & {x}_{6} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{3} & {b} \\\\\n",
"\\hline\n",
" {\\color{green}{s}}_{1} & 0 & 2 & 1 & 2 & 4 & 0 & 1 & 0 & 10 \\\\\n",
"{x}_{1} & 1 & 5 & 0 & -1 & 5 & 0 & 0 & 0 & 15 \\\\\n",
"{x}_{6} & 0 & 3 & 0 & -2 & 4 & 1 & 0 & -1 & 25 \\\\\n",
"\\hline\n",
" {Z_{ind}} & 0 & -18 & 3 & 8 & -18 & 0 & 0 & 2 & 95\n",
"\\end{array}\\right)$$"
],
"text/plain": [
"[ B| x1 x2 x3 x4 x5 x6 s1 s3|rhs]\n",
"[---+-------------------------------+---]\n",
"[ s1| 0 2 1 2 4 0 1 0| 10]\n",
"[ x1| 1 5 0 -1 5 0 0 0| 15]\n",
"[ x6| 0 3 0 -2 4 1 0 -1| 25]\n",
"[---+-------------------------------+---]\n",
"[ Z| 0 -18 3 8 -18 0 0 2| 95]"
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"source": [
"tipo ='min' # Problema de tipo max o min\n",
"\n",
"n=6 # número de variables x's\n",
"m=3 # número de restricciones (distintas de las de signo)\n",
"\n",
"c=matrix(QQ,1,n,[3,3,3,1,5,2] ) # vector de costos\n",
"\n",
"A=matrix(QQ,m,n,[ # coeficientes de las variables x's\n",
"[0,2,1,2,4,0],\n",
"[1,5,0,-1,5,0],\n",
"[0,3,0,-2,4,1]\n",
"])\n",
"\n",
"b=matrix(QQ,m,1,[10,15,25]) # vector de la derecha\n",
"\n",
"\n",
"h=matrix(ZZ,1,m,[1,0,-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",
"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=(7,1,6) # 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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"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrr|r}\n",
"{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {x}_{5} & {x}_{6} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{3} & {b} \\\\\n",
"\\hline\n",
" {x}_{5} & 0 & \\frac{1}{2} & \\frac{1}{4} & \\frac{1}{2} & 1 & 0 & \\frac{1}{4} & 0 & \\frac{5}{2} \\\\\n",
"{x}_{1} & 1 & \\frac{5}{2} & -\\frac{5}{4} & -\\frac{7}{2} & 0 & 0 & -\\frac{5}{4} & 0 & \\frac{5}{2} \\\\\n",
"{x}_{6} & 0 & 1 & -1 & -4 & 0 & 1 & -1 & -1 & 15 \\\\\n",
"\\hline\n",
" {Z_{ind}} & 0 & -9 & \\frac{15}{2} & 17 & 0 & 0 & \\frac{9}{2} & 2 & 50\n",
"\\end{array}\\right)$$"
],
"text/plain": [
"[ B| x1 x2 x3 x4 x5 x6 s1 s3| rhs]\n",
"[----+---------------------------------------+----]\n",
"[ x5| 0 1/2 1/4 1/2 1 0 1/4 0| 5/2]\n",
"[ x1| 1 5/2 -5/4 -7/2 0 0 -5/4 0| 5/2]\n",
"[ x6| 0 1 -1 -4 0 1 -1 -1| 15]\n",
"[----+---------------------------------------+----]\n",
"[ Z| 0 -9 15/2 17 0 0 9/2 2| 50]"
]
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"source": [
"cambio(1,5)"
]
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"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrr|r}\n",
"{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {x}_{5} & {x}_{6} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{3} & {b} \\\\\n",
"\\hline\n",
" {x}_{5} & -\\frac{1}{5} & 0 & \\frac{1}{2} & \\frac{6}{5} & 1 & 0 & \\frac{1}{2} & 0 & 2 \\\\\n",
"{x}_{2} & \\frac{2}{5} & 1 & -\\frac{1}{2} & -\\frac{7}{5} & 0 & 0 & -\\frac{1}{2} & 0 & 1 \\\\\n",
"{x}_{6} & -\\frac{2}{5} & 0 & -\\frac{1}{2} & -\\frac{13}{5} & 0 & 1 & -\\frac{1}{2} & -1 & 14 \\\\\n",
"\\hline\n",
" {Z_{ind}} & \\frac{18}{5} & 0 & 3 & \\frac{22}{5} & 0 & 0 & 0 & 2 & 41\n",
"\\end{array}\\right)$$"
],
"text/plain": [
"[ B| x1 x2 x3 x4 x5 x6 s1 s3| rhs]\n",
"[-----+-----------------------------------------------+-----]\n",
"[ x5| -1/5 0 1/2 6/5 1 0 1/2 0| 2]\n",
"[ x2| 2/5 1 -1/2 -7/5 0 0 -1/2 0| 1]\n",
"[ x6| -2/5 0 -1/2 -13/5 0 1 -1/2 -1| 14]\n",
"[-----+-----------------------------------------------+-----]\n",
"[ Z| 18/5 0 3 22/5 0 0 0 2| 41]"
]
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"source": [
"cambio(2,2)"
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