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"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{l}\n",
"\\begin{array}{lcrcrcrcrcrcrcrcl}\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} 6 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} x_{6} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 2 x_{7} \\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} 2 x_{2} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 3 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} x_{6} \\mspace{-6mu}&\\mspace{-6mu} - \\mspace{-6mu}&\\mspace{-6mu} 5 x_{7} \\mspace{-6mu}&\\mspace{-6mu} \\geq \\mspace{-6mu}&\\mspace{-6mu} 10 \\\\\n",
" \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} 2 x_{1} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 5 x_{2} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 6 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} x_{6} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 2 x_{7} \\mspace{-6mu}&\\mspace{-6mu} = \\mspace{-6mu}&\\mspace{-6mu} 15 \\\\\n",
" \\mspace{-6mu}&\\mspace{-6mu} - \\mspace{-6mu}&\\mspace{-6mu} x_{1} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 8 x_{2} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 9 x_{3} \\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} \\mspace{-6mu}&\\mspace{-6mu} - \\mspace{-6mu}&\\mspace{-6mu} 3 x_{7} \\mspace{-6mu}&\\mspace{-6mu} \\leq \\mspace{-6mu}&\\mspace{-6mu} 10 \\\\\n",
"\\end{array} \\\\\n",
"x_{1}, x_{2}, x_{3}, x_{4}, x_{5}, x_{6}, x_{7} \\geq 0\n",
"\\end{array}$$"
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"LP problem (use 'view(...)' or '%display typeset' for details)"
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"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}-15$$"
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"-15"
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"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(0,\\,0,\\,0,\\,0,\\,0,\\,15,\\,0\\right)$$"
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"(0, 0, 0, 0, 0, 15, 0)"
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"text/plain": [
"salto"
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"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$$"
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"text/latex": [
"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrr|r}\n",
"{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {x}_{5} & {x}_{6} & {x}_{7} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{3} & {\\color{red}{t}}_{1} & {\\color{red}{t}}_{2} & {b} \\\\\n",
"\\hline\n",
" {\\color{red}{t}}_{1} & 1 & 2 & 3 & 2 & 4 & 1 & -5 & -1 & 0 & 1 & 0 & 10 \\\\\n",
"{\\color{red}{t}}_{2} & 2 & 5 & 6 & -1 & 5 & 1 & 2 & 0 & 0 & 0 & 1 & 15 \\\\\n",
"{\\color{green}{s}}_{3} & -1 & 8 & 9 & 1 & -2 & 0 & -3 & 0 & 1 & 0 & 0 & 10 \\\\\n",
"\\hline\n",
" {W_{ind}} & -3 & -7 & -9 & -1 & -9 & -2 & 3 & 1 & 0 & 0 & 0 & 25\n",
"\\end{array}\\right)$$"
],
"text/plain": [
"[ B| x1 x2 x3 x4 x5 x6 x7 s1 s3 t1 t2|rhs]\n",
"[---+-------------------------------------------+---]\n",
"[ t1| 1 2 3 2 4 1 -5 -1 0 1 0| 10]\n",
"[ t2| 2 5 6 -1 5 1 2 0 0 0 1| 15]\n",
"[ s3| -1 8 9 1 -2 0 -3 0 1 0 0| 10]\n",
"[---+-------------------------------------------+---]\n",
"[ W| -3 -7 -9 -1 -9 -2 3 1 0 0 0| 25]"
]
},
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],
"source": [
"tipo='min' # Problema de tipo max o min\n",
"\n",
"n=7 # número de variables x's\n",
"m=3 # número de restricciones (distintas de las de signo)\n",
"\n",
"c=matrix(QQ,1,n,[1,5,6,2,3,-1,2] ) # vector de costos\n",
"\n",
"A=matrix(QQ,m,n,[ # coeficientes de las variables x's\n",
"[1,2,3,2,4,1,-5],\n",
"[2,5,6,-1,5,1,2],\n",
"[-1,8,9,1,-2,0,-3]\n",
"])\n",
"\n",
"b=matrix(QQ,m,1,[10,15,10]) # 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,[1,1,0]) # 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=(10,11,9) # 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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"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrr|r}\n",
"{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {x}_{5} & {x}_{6} & {x}_{7} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{3} & {\\color{red}{t}}_{1} & {\\color{red}{t}}_{2} & {b} \\\\\n",
"\\hline\n",
" {x}_{5} & \\frac{1}{4} & \\frac{1}{2} & \\frac{3}{4} & \\frac{1}{2} & 1 & \\frac{1}{4} & -\\frac{5}{4} & -\\frac{1}{4} & 0 & \\frac{1}{4} & 0 & \\frac{5}{2} \\\\\n",
"{\\color{red}{t}}_{2} & \\frac{3}{4} & \\frac{5}{2} & \\frac{9}{4} & -\\frac{7}{2} & 0 & -\\frac{1}{4} & \\frac{33}{4} & \\frac{5}{4} & 0 & -\\frac{5}{4} & 1 & \\frac{5}{2} \\\\\n",
"{\\color{green}{s}}_{3} & -\\frac{1}{2} & 9 & \\frac{21}{2} & 2 & 0 & \\frac{1}{2} & -\\frac{11}{2} & -\\frac{1}{2} & 1 & \\frac{1}{2} & 0 & 15 \\\\\n",
"\\hline\n",
" {W_{ind}} & -\\frac{3}{4} & -\\frac{5}{2} & -\\frac{9}{4} & \\frac{7}{2} & 0 & \\frac{1}{4} & -\\frac{33}{4} & -\\frac{5}{4} & 0 & \\frac{9}{4} & 0 & \\frac{5}{2}\n",
"\\end{array}\\right)$$"
],
"text/plain": [
"[ B| x1 x2 x3 x4 x5 x6 x7 s1 s3 t1 t2| rhs]\n",
"[-----+-----------------------------------------------------------------+-----]\n",
"[ x5| 1/4 1/2 3/4 1/2 1 1/4 -5/4 -1/4 0 1/4 0| 5/2]\n",
"[ t2| 3/4 5/2 9/4 -7/2 0 -1/4 33/4 5/4 0 -5/4 1| 5/2]\n",
"[ s3| -1/2 9 21/2 2 0 1/2 -11/2 -1/2 1 1/2 0| 15]\n",
"[-----+-----------------------------------------------------------------+-----]\n",
"[ W| -3/4 -5/2 -9/4 7/2 0 1/4 -33/4 -5/4 0 9/4 0| 5/2]"
]
},
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"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrr|r}\n",
"{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {x}_{5} & {x}_{6} & {x}_{7} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{3} & {\\color{red}{t}}_{1} & {\\color{red}{t}}_{2} & {b} \\\\\n",
"\\hline\n",
" {x}_{5} & \\frac{4}{11} & \\frac{29}{33} & \\frac{12}{11} & -\\frac{1}{33} & 1 & \\frac{7}{33} & 0 & -\\frac{2}{33} & 0 & \\frac{2}{33} & \\frac{5}{33} & \\frac{95}{33} \\\\\n",
"{x}_{7} & \\frac{1}{11} & \\frac{10}{33} & \\frac{3}{11} & -\\frac{14}{33} & 0 & -\\frac{1}{33} & 1 & \\frac{5}{33} & 0 & -\\frac{5}{33} & \\frac{4}{33} & \\frac{10}{33} \\\\\n",
"{\\color{green}{s}}_{3} & 0 & \\frac{32}{3} & 12 & -\\frac{1}{3} & 0 & \\frac{1}{3} & 0 & \\frac{1}{3} & 1 & -\\frac{1}{3} & \\frac{2}{3} & \\frac{50}{3} \\\\\n",
"\\hline\n",
" {W_{ind}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0\n",
"\\end{array}\\right)$$"
],
"text/plain": [
"[ B| x1 x2 x3 x4 x5 x6 x7 s1 s3 t1 t2| rhs]\n",
"[------+----------------------------------------------------------------------------+------]\n",
"[ x5| 4/11 29/33 12/11 -1/33 1 7/33 0 -2/33 0 2/33 5/33| 95/33]\n",
"[ x7| 1/11 10/33 3/11 -14/33 0 -1/33 1 5/33 0 -5/33 4/33| 10/33]\n",
"[ s3| 0 32/3 12 -1/3 0 1/3 0 1/3 1 -1/3 2/3| 50/3]\n",
"[------+----------------------------------------------------------------------------+------]\n",
"[ W| 0 0 0 0 0 0 0 0 0 1 1| 0]"
]
},
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},
{
"data": {
"text/html": [
""
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"text/latex": [
"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrr|r}\n",
"{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {x}_{5} & {x}_{6} & {x}_{7} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{3} & {b} \\\\\n",
"\\hline\n",
" {x}_{5} & \\frac{4}{11} & \\frac{29}{33} & \\frac{12}{11} & -\\frac{1}{33} & 1 & \\frac{7}{33} & 0 & -\\frac{2}{33} & 0 & \\frac{95}{33} \\\\\n",
"{x}_{7} & \\frac{1}{11} & \\frac{10}{33} & \\frac{3}{11} & -\\frac{14}{33} & 0 & -\\frac{1}{33} & 1 & \\frac{5}{33} & 0 & \\frac{10}{33} \\\\\n",
"{\\color{green}{s}}_{3} & 0 & \\frac{32}{3} & 12 & -\\frac{1}{3} & 0 & \\frac{1}{3} & 0 & \\frac{1}{3} & 1 & \\frac{50}{3} \\\\\n",
"\\hline\n",
" {Z_{ind}} & -\\frac{3}{11} & \\frac{58}{33} & \\frac{24}{11} & \\frac{97}{33} & 0 & -\\frac{52}{33} & 0 & -\\frac{4}{33} & 0 & \\frac{305}{33}\n",
"\\end{array}\\right)$$"
],
"text/plain": [
"[ B| x1 x2 x3 x4 x5 x6 x7 s1 s3| rhs]\n",
"[------+--------------------------------------------------------------+------]\n",
"[ x5| 4/11 29/33 12/11 -1/33 1 7/33 0 -2/33 0| 95/33]\n",
"[ x7| 1/11 10/33 3/11 -14/33 0 -1/33 1 5/33 0| 10/33]\n",
"[ s3| 0 32/3 12 -1/3 0 1/3 0 1/3 1| 50/3]\n",
"[------+--------------------------------------------------------------+------]\n",
"[ Z| -3/11 58/33 24/11 97/33 0 -52/33 0 -4/33 0|305/33]"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"cambio(1,5); cambio(2,7); tt=[0,0,0];faseII(0,tt);"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"# cocientes(4) # Si el problema es de tipo maximizar sería no acotado"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [],
"source": [
"#cambio(1,6)"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"scrolled": false
},
"outputs": [
{
"data": {
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"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrr|r}\n",
"{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {x}_{5} & {x}_{6} & {x}_{7} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{3} & {b} \\\\\n",
"\\hline\n",
" {x}_{6} & \\frac{12}{7} & \\frac{29}{7} & \\frac{36}{7} & -\\frac{1}{7} & \\frac{33}{7} & 1 & 0 & -\\frac{2}{7} & 0 & \\frac{95}{7} \\\\\n",
"{x}_{7} & \\frac{1}{7} & \\frac{3}{7} & \\frac{3}{7} & -\\frac{3}{7} & \\frac{1}{7} & 0 & 1 & \\frac{1}{7} & 0 & \\frac{5}{7} \\\\\n",
"{\\color{green}{s}}_{3} & -\\frac{4}{7} & \\frac{65}{7} & \\frac{72}{7} & -\\frac{2}{7} & -\\frac{11}{7} & 0 & 0 & \\frac{3}{7} & 1 & \\frac{85}{7} \\\\\n",
"\\hline\n",
" {Z_{ind}} & \\frac{17}{7} & \\frac{58}{7} & \\frac{72}{7} & \\frac{19}{7} & \\frac{52}{7} & 0 & 0 & -\\frac{4}{7} & 0 & -\\frac{85}{7}\n",
"\\end{array}\\right)$$"
],
"text/plain": [
"[ B| x1 x2 x3 x4 x5 x6 x7 s1 s3| rhs]\n",
"[-----+-----------------------------------------------------+-----]\n",
"[ x6| 12/7 29/7 36/7 -1/7 33/7 1 0 -2/7 0| 95/7]\n",
"[ x7| 1/7 3/7 3/7 -3/7 1/7 0 1 1/7 0| 5/7]\n",
"[ s3| -4/7 65/7 72/7 -2/7 -11/7 0 0 3/7 1| 85/7]\n",
"[-----+-----------------------------------------------------+-----]\n",
"[ Z| 17/7 58/7 72/7 19/7 52/7 0 0 -4/7 0|-85/7]"
]
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"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrr|r}\n",
"{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {x}_{5} & {x}_{6} & {x}_{7} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{3} & {b} \\\\\n",
"\\hline\n",
" {x}_{6} & \\frac{12}{7} & \\frac{29}{7} & \\frac{36}{7} & -\\frac{1}{7} & \\frac{33}{7} & 1 & 0 & -\\frac{2}{7} & 0 & \\frac{95}{7} \\\\\n",
"{x}_{7} & \\frac{1}{7} & \\frac{3}{7} & \\frac{3}{7} & -\\frac{3}{7} & \\frac{1}{7} & 0 & 1 & \\frac{1}{7} & 0 & \\frac{5}{7} \\\\\n",
"{\\color{green}{s}}_{3} & -\\frac{4}{7} & \\frac{65}{7} & \\frac{72}{7} & -\\frac{2}{7} & -\\frac{11}{7} & 0 & 0 & \\frac{3}{7} & 1 & \\frac{85}{7} \\\\\n",
"\\hline\n",
" {Z_{ind}} & \\frac{17}{7} & \\frac{58}{7} & \\frac{72}{7} & \\frac{19}{7} & \\frac{52}{7} & 0 & 0 & -\\frac{4}{7} & 0 & -\\frac{85}{7}\n",
"\\end{array}\\right)$$"
],
"text/plain": [
"[ B| x1 x2 x3 x4 x5 x6 x7 s1 s3| rhs]\n",
"[-----+-----------------------------------------------------+-----]\n",
"[ x6| 12/7 29/7 36/7 -1/7 33/7 1 0 -2/7 0| 95/7]\n",
"[ x7| 1/7 3/7 3/7 -3/7 1/7 0 1 1/7 0| 5/7]\n",
"[ s3| -4/7 65/7 72/7 -2/7 -11/7 0 0 3/7 1| 85/7]\n",
"[-----+-----------------------------------------------------+-----]\n",
"[ Z| 17/7 58/7 72/7 19/7 52/7 0 0 -4/7 0|-85/7]"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
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"text/latex": [
"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrr|r}\n",
"{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {x}_{5} & {x}_{6} & {x}_{7} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{3} & {b} \\\\\n",
"\\hline\n",
" {x}_{6} & \\frac{128}{65} & 0 & \\frac{36}{65} & -\\frac{1}{65} & \\frac{352}{65} & 1 & 0 & -\\frac{31}{65} & -\\frac{29}{65} & \\frac{106}{13} \\\\\n",
"{x}_{7} & \\frac{11}{65} & 0 & -\\frac{3}{65} & -\\frac{27}{65} & \\frac{14}{65} & 0 & 1 & \\frac{8}{65} & -\\frac{3}{65} & \\frac{2}{13} \\\\\n",
"{x}_{2} & -\\frac{4}{65} & 1 & \\frac{72}{65} & -\\frac{2}{65} & -\\frac{11}{65} & 0 & 0 & \\frac{3}{65} & \\frac{7}{65} & \\frac{17}{13} \\\\\n",
"\\hline\n",
" {Z_{ind}} & \\frac{191}{65} & 0 & \\frac{72}{65} & \\frac{193}{65} & \\frac{574}{65} & 0 & 0 & -\\frac{62}{65} & -\\frac{58}{65} & -\\frac{17}{13}\n",
"\\end{array}\\right)$$"
],
"text/plain": [
"[ B| x1 x2 x3 x4 x5 x6 x7 s1 s3| rhs]\n",
"[------+--------------------------------------------------------------+------]\n",
"[ x6|128/65 0 36/65 -1/65 352/65 1 0 -31/65 -29/65|106/13]\n",
"[ x7| 11/65 0 -3/65 -27/65 14/65 0 1 8/65 -3/65| 2/13]\n",
"[ x2| -4/65 1 72/65 -2/65 -11/65 0 0 3/65 7/65| 17/13]\n",
"[------+--------------------------------------------------------------+------]\n",
"[ Z|191/65 0 72/65 193/65 574/65 0 0 -62/65 -58/65|-17/13]"
]
},
"metadata": {},
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{
"data": {
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"text/latex": [
"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrr|r}\n",
"{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {x}_{5} & {x}_{6} & {x}_{7} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{3} & {b} \\\\\n",
"\\hline\n",
" {x}_{6} & \\frac{21}{8} & 0 & \\frac{3}{8} & -\\frac{13}{8} & \\frac{25}{4} & 1 & \\frac{31}{8} & 0 & -\\frac{5}{8} & \\frac{35}{4} \\\\\n",
"{\\color{green}{s}}_{1} & \\frac{11}{8} & 0 & -\\frac{3}{8} & -\\frac{27}{8} & \\frac{7}{4} & 0 & \\frac{65}{8} & 1 & -\\frac{3}{8} & \\frac{5}{4} \\\\\n",
"{x}_{2} & -\\frac{1}{8} & 1 & \\frac{9}{8} & \\frac{1}{8} & -\\frac{1}{4} & 0 & -\\frac{3}{8} & 0 & \\frac{1}{8} & \\frac{5}{4} \\\\\n",
"\\hline\n",
" {Z_{ind}} & \\frac{17}{4} & 0 & \\frac{3}{4} & -\\frac{1}{4} & \\frac{21}{2} & 0 & \\frac{31}{4} & 0 & -\\frac{5}{4} & -\\frac{5}{2}\n",
"\\end{array}\\right)$$"
],
"text/plain": [
"[ B| x1 x2 x3 x4 x5 x6 x7 s1 s3| rhs]\n",
"[-----+-----------------------------------------------------+-----]\n",
"[ x6| 21/8 0 3/8 -13/8 25/4 1 31/8 0 -5/8| 35/4]\n",
"[ s1| 11/8 0 -3/8 -27/8 7/4 0 65/8 1 -3/8| 5/4]\n",
"[ x2| -1/8 1 9/8 1/8 -1/4 0 -3/8 0 1/8| 5/4]\n",
"[-----+-----------------------------------------------------+-----]\n",
"[ Z| 17/4 0 3/4 -1/4 21/2 0 31/4 0 -5/4| -5/2]"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/html": [
""
],
"text/latex": [
"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrr|r}\n",
"{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {x}_{5} & {x}_{6} & {x}_{7} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{3} & {b} \\\\\n",
"\\hline\n",
" {x}_{6} & 2 & 5 & 6 & -1 & 5 & 1 & 2 & 0 & 0 & 15 \\\\\n",
"{\\color{green}{s}}_{1} & 1 & 3 & 3 & -3 & 1 & 0 & 7 & 1 & 0 & 5 \\\\\n",
"{\\color{green}{s}}_{3} & -1 & 8 & 9 & 1 & -2 & 0 & -3 & 0 & 1 & 10 \\\\\n",
"\\hline\n",
" {Z_{ind}} & 3 & 10 & 12 & 1 & 8 & 0 & 4 & 0 & 0 & -15\n",
"\\end{array}\\right)$$"
],
"text/plain": [
"[ B| x1 x2 x3 x4 x5 x6 x7 s1 s3|rhs]\n",
"[---+-----------------------------------+---]\n",
"[ x6| 2 5 6 -1 5 1 2 0 0| 15]\n",
"[ s1| 1 3 3 -3 1 0 7 1 0| 5]\n",
"[ s3| -1 8 9 1 -2 0 -3 0 1| 10]\n",
"[---+-----------------------------------+---]\n",
"[ Z| 3 10 12 1 8 0 4 0 0|-15]"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"cambio(1,6);cambio(2,7);cambio(3,2);cambio(2,8);cambio(3,9) # si el problema es de tipo minimizar"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"El problema es óptimo. El valor óptimo de la $z$ es 15 y se alcanza en $x=(0,0,0,0,0,15,0)$"
]
}
],
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