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" \\max \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} 10 x_{1} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 14 x_{2} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 12 x_{3} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 18 x_{4} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 20 x_{5} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 16 x_{6} \\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} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 3 x_{4} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 2 x_{5} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} x_{6} \\mspace{-6mu}&\\mspace{-6mu} \\leq \\mspace{-6mu}&\\mspace{-6mu} 26 \\\\\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} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 3 x_{4} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 2 x_{5} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} x_{6} \\mspace{-6mu}&\\mspace{-6mu} \\leq \\mspace{-6mu}&\\mspace{-6mu} 32 \\\\\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} x_{3} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} x_{4} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} x_{5} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\leq \\mspace{-6mu}&\\mspace{-6mu} 25 \\\\\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} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 2 x_{5} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 2 x_{6} \\mspace{-6mu}&\\mspace{-6mu} \\geq \\mspace{-6mu}&\\mspace{-6mu} 30 \\\\\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} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} x_{6} \\mspace{-6mu}&\\mspace{-6mu} \\leq \\mspace{-6mu}&\\mspace{-6mu} 14 \\\\\n",
"\\end{array} \\\\\n",
"x_{1}, x_{2}, x_{3}, x_{4}, x_{5}, x_{6} \\geq 0\n",
"\\end{array}$$"
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"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{l}\n",
"\\begin{array}{lcrcrcrcrcrcl}\n",
" \\min \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} 26 y_{1} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 32 y_{2} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 25 y_{3} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 30 y_{4} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 14 y_{5} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\\\\n",
" \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} y_{1} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} y_{2} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} y_{3} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} y_{5} \\mspace{-6mu}&\\mspace{-6mu} \\geq \\mspace{-6mu}&\\mspace{-6mu} 10 \\\\\n",
" \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} 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} \\geq \\mspace{-6mu}&\\mspace{-6mu} 14 \\\\\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} y_{3} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 2 y_{4} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\geq \\mspace{-6mu}&\\mspace{-6mu} 12 \\\\\n",
" \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} 3 y_{1} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 3 y_{2} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} y_{3} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} y_{5} \\mspace{-6mu}&\\mspace{-6mu} \\geq \\mspace{-6mu}&\\mspace{-6mu} 18 \\\\\n",
" \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} 2 y_{1} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 2 y_{2} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} y_{3} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 2 y_{4} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\geq \\mspace{-6mu}&\\mspace{-6mu} 20 \\\\\n",
" \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} y_{1} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} y_{2} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 2 y_{4} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} y_{5} \\mspace{-6mu}&\\mspace{-6mu} \\geq \\mspace{-6mu}&\\mspace{-6mu} 16 \\\\\n",
"\\end{array} \\\\\n",
"y_{1} \\geq 0,\\ y_{2} \\geq 0,\\ y_{3} \\geq 0,\\ y_{4} \\leq 0,\\ y_{5} \\geq 0\n",
"\\end{array}$$"
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"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{\\ \\ \\ Fase\\ I}$$"
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"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrrr|r}\n",
"{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {x}_{5} & {x}_{6} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{red}{t}}_{4} & {b} \\\\\n",
"\\hline\n",
" {\\color{green}{s}}_{1} & 1 & 1 & 0 & 3 & 2 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 26 \\\\\n",
"{\\color{green}{s}}_{2} & 1 & 1 & 0 & 3 & 2 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 32 \\\\\n",
"{\\color{green}{s}}_{3} & 1 & 2 & 1 & 1 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 25 \\\\\n",
"{\\color{red}{t}}_{4} & 0 & 1 & 2 & 0 & 2 & 2 & 0 & 0 & 0 & -1 & 0 & 1 & 30 \\\\\n",
"{\\color{green}{s}}_{5} & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 14 \\\\\n",
"\\hline\n",
" {W_{ind}} & 0 & -1 & -2 & 0 & -2 & -2 & 0 & 0 & 0 & 1 & 0 & 0 & 30\n",
"\\end{array}\\right)$$"
],
"text/plain": [
"[ B| x1 x2 x3 x4 x5 x6 s1 s2 s3 s4 s5 t4|rhs]\n",
"[---+-----------------------------------------------+---]\n",
"[ s1| 1 1 0 3 2 1 1 0 0 0 0 0| 26]\n",
"[ s2| 1 1 0 3 2 1 0 1 0 0 0 0| 32]\n",
"[ s3| 1 2 1 1 1 0 0 0 1 0 0 0| 25]\n",
"[ t4| 0 1 2 0 2 2 0 0 0 -1 0 1| 30]\n",
"[ s5| 1 0 0 1 0 1 0 0 0 0 1 0| 14]\n",
"[---+-----------------------------------------------+---]\n",
"[ W| 0 -1 -2 0 -2 -2 0 0 0 1 0 0| 30]"
]
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"source": [
"tipo='max' # Problema de tipo max o min\n",
"\n",
"n=6 # número de variables x's\n",
"m=5 # número de restricciones (distintas de las de signo)\n",
"\n",
"c=matrix(QQ,1,n,[10,14,12,18,20,16] ) # vector de costos\n",
"\n",
"A=matrix(QQ,m,n,[ # coeficientes de las variables x's\n",
"[1,1,0,3,2,1],\n",
"[1,1,0,3,2,1],\n",
"[1,2,1,1,1,0],\n",
"[0,1,2,0,2,2],\n",
"[1,0,0,1,0,1]\n",
"])\n",
"\n",
"b=matrix(QQ,m,1,[26,32,25,30,14]) # vector de la derecha\n",
"\n",
"\n",
"######################################################\n",
"############### VARIABLES DE HOLGURA ################\n",
"\n",
"\n",
"h=matrix(ZZ,1,m,[1,1,1,-1,1]) # variables de holgura: \n",
" # Pon 1 si va sumando, \n",
" # -1 si va restando y \n",
" # 0 si no hay variable de holgura.\n",
"\n",
"\n",
"####################################################################\n",
"############ HASTA AQUÍ LOS DATOS ################################\n",
"####################################################################\n",
"\n",
"\n",
"\n",
"\n",
"load('https://sage.unex.es/501708/simplex2023Manual.sage')\n"
]
},
{
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"execution_count": 3,
"metadata": {},
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"source": [
"# cambio(4,3);tt=[0,0,0,0,0];faseII(0,tt); Descomentar si es de tipo minimizar"
]
},
{
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"execution_count": 4,
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"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrrr|r}\n",
"{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {x}_{5} & {x}_{6} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{red}{t}}_{4} & {b} \\\\\n",
"\\hline\n",
" {\\color{green}{s}}_{1} & 1 & 1 & 0 & 3 & 2 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 26 \\\\\n",
"{\\color{green}{s}}_{2} & 1 & 1 & 0 & 3 & 2 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 32 \\\\\n",
"{\\color{green}{s}}_{3} & 1 & \\frac{3}{2} & 0 & 1 & 0 & -1 & 0 & 0 & 1 & \\frac{1}{2} & 0 & -\\frac{1}{2} & 10 \\\\\n",
"{x}_{3} & 0 & \\frac{1}{2} & 1 & 0 & 1 & 1 & 0 & 0 & 0 & -\\frac{1}{2} & 0 & \\frac{1}{2} & 15 \\\\\n",
"{\\color{green}{s}}_{5} & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 14 \\\\\n",
"\\hline\n",
" {W_{ind}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0\n",
"\\end{array}\\right)$$"
],
"text/plain": [
"[ B| x1 x2 x3 x4 x5 x6 s1 s2 s3 s4 s5 t4| rhs]\n",
"[----+-----------------------------------------------------------+----]\n",
"[ s1| 1 1 0 3 2 1 1 0 0 0 0 0| 26]\n",
"[ s2| 1 1 0 3 2 1 0 1 0 0 0 0| 32]\n",
"[ s3| 1 3/2 0 1 0 -1 0 0 1 1/2 0 -1/2| 10]\n",
"[ x3| 0 1/2 1 0 1 1 0 0 0 -1/2 0 1/2| 15]\n",
"[ s5| 1 0 0 1 0 1 0 0 0 0 1 0| 14]\n",
"[----+-----------------------------------------------------------+----]\n",
"[ W| 0 0 0 0 0 0 0 0 0 0 0 1| 0]"
]
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"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrr|r}\n",
"{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {x}_{5} & {x}_{6} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {b} \\\\\n",
"\\hline\n",
" {\\color{green}{s}}_{1} & 1 & 1 & 0 & 3 & 2 & 1 & 1 & 0 & 0 & 0 & 0 & 26 \\\\\n",
"{\\color{green}{s}}_{2} & 1 & 1 & 0 & 3 & 2 & 1 & 0 & 1 & 0 & 0 & 0 & 32 \\\\\n",
"{\\color{green}{s}}_{3} & 1 & \\frac{3}{2} & 0 & 1 & 0 & -1 & 0 & 0 & 1 & \\frac{1}{2} & 0 & 10 \\\\\n",
"{x}_{3} & 0 & \\frac{1}{2} & 1 & 0 & 1 & 1 & 0 & 0 & 0 & -\\frac{1}{2} & 0 & 15 \\\\\n",
"{\\color{green}{s}}_{5} & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 14 \\\\\n",
"\\hline\n",
" {Z_{ind}} & 10 & 8 & 0 & 18 & 8 & 4 & 0 & 0 & 0 & 6 & 0 & 180\n",
"\\end{array}\\right)$$"
],
"text/plain": [
"[ B| x1 x2 x3 x4 x5 x6 s1 s2 s3 s4 s5| rhs]\n",
"[----+------------------------------------------------------+----]\n",
"[ s1| 1 1 0 3 2 1 1 0 0 0 0| 26]\n",
"[ s2| 1 1 0 3 2 1 0 1 0 0 0| 32]\n",
"[ s3| 1 3/2 0 1 0 -1 0 0 1 1/2 0| 10]\n",
"[ x3| 0 1/2 1 0 1 1 0 0 0 -1/2 0| 15]\n",
"[ s5| 1 0 0 1 0 1 0 0 0 0 1| 14]\n",
"[----+------------------------------------------------------+----]\n",
"[ Z| 10 8 0 18 8 4 0 0 0 6 0| 180]"
]
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"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrr|r}\n",
"{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {x}_{5} & {x}_{6} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {b} \\\\\n",
"\\hline\n",
" {x}_{4} & \\frac{1}{3} & \\frac{1}{3} & 0 & 1 & \\frac{2}{3} & \\frac{1}{3} & \\frac{1}{3} & 0 & 0 & 0 & 0 & \\frac{26}{3} \\\\\n",
"{\\color{green}{s}}_{2} & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 1 & 0 & 0 & 0 & 6 \\\\\n",
"{\\color{green}{s}}_{3} & \\frac{2}{3} & \\frac{7}{6} & 0 & 0 & -\\frac{2}{3} & -\\frac{4}{3} & -\\frac{1}{3} & 0 & 1 & \\frac{1}{2} & 0 & \\frac{4}{3} \\\\\n",
"{x}_{3} & 0 & \\frac{1}{2} & 1 & 0 & 1 & 1 & 0 & 0 & 0 & -\\frac{1}{2} & 0 & 15 \\\\\n",
"{\\color{green}{s}}_{5} & \\frac{2}{3} & -\\frac{1}{3} & 0 & 0 & -\\frac{2}{3} & \\frac{2}{3} & -\\frac{1}{3} & 0 & 0 & 0 & 1 & \\frac{16}{3} \\\\\n",
"\\hline\n",
" {Z_{ind}} & 4 & 2 & 0 & 0 & -4 & -2 & -6 & 0 & 0 & 6 & 0 & 336\n",
"\\end{array}\\right)$$"
],
"text/plain": [
"[ B| x1 x2 x3 x4 x5 x6 s1 s2 s3 s4 s5| rhs]\n",
"[----+------------------------------------------------------+----]\n",
"[ x4| 1/3 1/3 0 1 2/3 1/3 1/3 0 0 0 0|26/3]\n",
"[ s2| 0 0 0 0 0 0 -1 1 0 0 0| 6]\n",
"[ s3| 2/3 7/6 0 0 -2/3 -4/3 -1/3 0 1 1/2 0| 4/3]\n",
"[ x3| 0 1/2 1 0 1 1 0 0 0 -1/2 0| 15]\n",
"[ s5| 2/3 -1/3 0 0 -2/3 2/3 -1/3 0 0 0 1|16/3]\n",
"[----+------------------------------------------------------+----]\n",
"[ Z| 4 2 0 0 -4 -2 -6 0 0 6 0| 336]"
]
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"text/latex": [
"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrr|r}\n",
"{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {x}_{5} & {x}_{6} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {b} \\\\\n",
"\\hline\n",
" {x}_{4} & \\frac{1}{3} & \\frac{1}{3} & 0 & 1 & \\frac{2}{3} & \\frac{1}{3} & \\frac{1}{3} & 0 & 0 & 0 & 0 & \\frac{26}{3} \\\\\n",
"{\\color{green}{s}}_{2} & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 1 & 0 & 0 & 0 & 6 \\\\\n",
"{\\color{green}{s}}_{4} & \\frac{4}{3} & \\frac{7}{3} & 0 & 0 & -\\frac{4}{3} & -\\frac{8}{3} & -\\frac{2}{3} & 0 & 2 & 1 & 0 & \\frac{8}{3} \\\\\n",
"{x}_{3} & \\frac{2}{3} & \\frac{5}{3} & 1 & 0 & \\frac{1}{3} & -\\frac{1}{3} & -\\frac{1}{3} & 0 & 1 & 0 & 0 & \\frac{49}{3} \\\\\n",
"{\\color{green}{s}}_{5} & \\frac{2}{3} & -\\frac{1}{3} & 0 & 0 & -\\frac{2}{3} & \\frac{2}{3} & -\\frac{1}{3} & 0 & 0 & 0 & 1 & \\frac{16}{3} \\\\\n",
"\\hline\n",
" {Z_{ind}} & -4 & -12 & 0 & 0 & 4 & 14 & -2 & 0 & -12 & 0 & 0 & 352\n",
"\\end{array}\\right)$$"
],
"text/plain": [
"[ B| x1 x2 x3 x4 x5 x6 s1 s2 s3 s4 s5| rhs]\n",
"[----+------------------------------------------------------+----]\n",
"[ x4| 1/3 1/3 0 1 2/3 1/3 1/3 0 0 0 0|26/3]\n",
"[ s2| 0 0 0 0 0 0 -1 1 0 0 0| 6]\n",
"[ s4| 4/3 7/3 0 0 -4/3 -8/3 -2/3 0 2 1 0| 8/3]\n",
"[ x3| 2/3 5/3 1 0 1/3 -1/3 -1/3 0 1 0 0|49/3]\n",
"[ s5| 2/3 -1/3 0 0 -2/3 2/3 -1/3 0 0 0 1|16/3]\n",
"[----+------------------------------------------------------+----]\n",
"[ Z| -4 -12 0 0 4 14 -2 0 -12 0 0| 352]"
]
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"text/latex": [
"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrr|r}\n",
"{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {x}_{5} & {x}_{6} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {b} \\\\\n",
"\\hline\n",
" {x}_{4} & 0 & \\frac{1}{2} & 0 & 1 & 1 & 0 & \\frac{1}{2} & 0 & 0 & 0 & -\\frac{1}{2} & 6 \\\\\n",
"{\\color{green}{s}}_{2} & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 1 & 0 & 0 & 0 & 6 \\\\\n",
"{\\color{green}{s}}_{4} & 4 & 1 & 0 & 0 & -4 & 0 & -2 & 0 & 2 & 1 & 4 & 24 \\\\\n",
"{x}_{3} & 1 & \\frac{3}{2} & 1 & 0 & 0 & 0 & -\\frac{1}{2} & 0 & 1 & 0 & \\frac{1}{2} & 19 \\\\\n",
"{x}_{6} & 1 & -\\frac{1}{2} & 0 & 0 & -1 & 1 & -\\frac{1}{2} & 0 & 0 & 0 & \\frac{3}{2} & 8 \\\\\n",
"\\hline\n",
" {Z_{ind}} & -18 & -5 & 0 & 0 & 18 & 0 & 5 & 0 & -12 & 0 & -21 & 464\n",
"\\end{array}\\right)$$"
],
"text/plain": [
"[ B| x1 x2 x3 x4 x5 x6 s1 s2 s3 s4 s5| rhs]\n",
"[----+------------------------------------------------------+----]\n",
"[ x4| 0 1/2 0 1 1 0 1/2 0 0 0 -1/2| 6]\n",
"[ s2| 0 0 0 0 0 0 -1 1 0 0 0| 6]\n",
"[ s4| 4 1 0 0 -4 0 -2 0 2 1 4| 24]\n",
"[ x3| 1 3/2 1 0 0 0 -1/2 0 1 0 1/2| 19]\n",
"[ x6| 1 -1/2 0 0 -1 1 -1/2 0 0 0 3/2| 8]\n",
"[----+------------------------------------------------------+----]\n",
"[ Z| -18 -5 0 0 18 0 5 0 -12 0 -21| 464]"
]
},
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},
{
"data": {
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"text/latex": [
"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrr|r}\n",
"{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {x}_{5} & {x}_{6} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {b} \\\\\n",
"\\hline\n",
" {x}_{5} & 0 & \\frac{1}{2} & 0 & 1 & 1 & 0 & \\frac{1}{2} & 0 & 0 & 0 & -\\frac{1}{2} & 6 \\\\\n",
"{\\color{green}{s}}_{2} & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 1 & 0 & 0 & 0 & 6 \\\\\n",
"{\\color{green}{s}}_{4} & 4 & 3 & 0 & 4 & 0 & 0 & 0 & 0 & 2 & 1 & 2 & 48 \\\\\n",
"{x}_{3} & 1 & \\frac{3}{2} & 1 & 0 & 0 & 0 & -\\frac{1}{2} & 0 & 1 & 0 & \\frac{1}{2} & 19 \\\\\n",
"{x}_{6} & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 14 \\\\\n",
"\\hline\n",
" {Z_{ind}} & -18 & -14 & 0 & -18 & 0 & 0 & -4 & 0 & -12 & 0 & -12 & 572\n",
"\\end{array}\\right)$$"
],
"text/plain": [
"[ B| x1 x2 x3 x4 x5 x6 s1 s2 s3 s4 s5| rhs]\n",
"[----+------------------------------------------------------+----]\n",
"[ x5| 0 1/2 0 1 1 0 1/2 0 0 0 -1/2| 6]\n",
"[ s2| 0 0 0 0 0 0 -1 1 0 0 0| 6]\n",
"[ s4| 4 3 0 4 0 0 0 0 2 1 2| 48]\n",
"[ x3| 1 3/2 1 0 0 0 -1/2 0 1 0 1/2| 19]\n",
"[ x6| 1 0 0 1 0 1 0 0 0 0 1| 14]\n",
"[----+------------------------------------------------------+----]\n",
"[ Z| -18 -14 0 -18 0 0 -4 0 -12 0 -12| 572]"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"cambio(4,3);tt=[0,0,0,0,0];faseII(0,tt);cambio(1,4);cambio(3,10);cambio(5,6);cambio(1,5)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Cuadro óptimo. Solución: $$x=(0,0,19,0,6,14); s=(0,6,0,48,0); z_{opt}=572$$"
]
},
{
"cell_type": "code",
"execution_count": null,
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"outputs": [],
"source": []
}
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