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"(0, 16/5, 13/2, 59/10)"
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"\\begin{array}{lcrcrcrcl}\n",
" \\min \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} 15 y_{1} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 16 y_{2} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 14 y_{3} \\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} 6 y_{2} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 4 y_{3} \\mspace{-6mu}&\\mspace{-6mu} \\geq \\mspace{-6mu}&\\mspace{-6mu} 7 \\\\\n",
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"\\end{array} \\\\\n",
"y_{1}, y_{2}, y_{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} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {b} \\\\\n",
"\\hline\n",
" {\\color{green}{s}}_{1} & 1 & 6 & -7 & 7 & 1 & 0 & 0 & 15 \\\\\n",
"{\\color{green}{s}}_{2} & 6 & -7 & 5 & 1 & 0 & 1 & 0 & 16 \\\\\n",
"{\\color{green}{s}}_{3} & 4 & 4 & 2 & -2 & 0 & 0 & 1 & 14 \\\\\n",
"\\hline\n",
" {Z_{ind}} & 7 & 12 & 17 & 12 & 0 & 0 & 0 & 0\n",
"\\end{array}\\right)$$"
],
"text/plain": [
"[ B| x1 x2 x3 x4 s1 s2 s3|rhs]\n",
"[---+---------------------------+---]\n",
"[ s1| 1 6 -7 7 1 0 0| 15]\n",
"[ s2| 6 -7 5 1 0 1 0| 16]\n",
"[ s3| 4 4 2 -2 0 0 1| 14]\n",
"[---+---------------------------+---]\n",
"[ Z| 7 12 17 12 0 0 0| 0]"
]
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"text": [
" \n",
"(Es un problema de tipo maximizar)\n",
" \n",
"cambio( 2 , 3 )\n",
"cambio( 3 , 2 )\n",
"cambio( 1 , 4 )\n"
]
},
{
"data": {
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"text/latex": [
"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrr|r}\n",
"{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {b} \\\\\n",
"\\hline\n",
" {x}_{4} & \\frac{35}{24} & 0 & 0 & 1 & \\frac{17}{120} & \\frac{1}{6} & \\frac{19}{240} & \\frac{59}{10} \\\\\n",
"{x}_{3} & \\frac{47}{24} & 0 & 1 & 0 & \\frac{1}{24} & \\frac{1}{6} & \\frac{11}{48} & \\frac{13}{2} \\\\\n",
"{x}_{2} & \\frac{3}{4} & 1 & 0 & 0 & \\frac{1}{20} & 0 & \\frac{7}{40} & \\frac{16}{5} \\\\\n",
"\\hline\n",
" {Z_{ind}} & -\\frac{1267}{24} & 0 & 0 & 0 & -\\frac{361}{120} & -\\frac{29}{6} & -\\frac{1667}{240} & \\frac{2197}{10}\n",
"\\end{array}\\right)$$"
],
"text/plain": [
"[ B| x1 x2 x3 x4 s1 s2 s3| rhs]\n",
"[---------+---------------------------------------------------------------------+---------]\n",
"[ x4| 35/24 0 0 1 17/120 1/6 19/240| 59/10]\n",
"[ x3| 47/24 0 1 0 1/24 1/6 11/48| 13/2]\n",
"[ x2| 3/4 1 0 0 1/20 0 7/40| 16/5]\n",
"[---------+---------------------------------------------------------------------+---------]\n",
"[ Z| -1267/24 0 0 0 -361/120 -29/6 -1667/240| 2197/10]"
]
},
"metadata": {},
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},
{
"name": "stdout",
"output_type": "stream",
"text": [
"El problema es óptimo\n"
]
}
],
"source": [
"tipo='max' #max o min\n",
"n=4 # número de variables x's\n",
"m=3 # número de restricciones (distintas de las de signo)\n",
"\n",
"\n",
"c=matrix(QQ,1,n,[7,12,17,12] ) # vector de costos\n",
"\n",
"A=matrix(QQ,m,n,[ # coeficientes de las variables x's\n",
"[1,6,-7,7],\n",
"[6,-7,5,1],\n",
"[4,4,2,-2]\n",
"])\n",
"\n",
"b=matrix(QQ,m,1,[15,16,14]) # vector de la derecha\n",
"\n",
"\n",
"\n",
"######################################################\n",
"############### VARIABLES DE HOLGURA ################\n",
"\n",
"\n",
"h=matrix(ZZ,1,m,[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",
"####################################################################\n",
"############ HASTA AQUÍ LOS DATOS ################################\n",
"####################################################################\n",
"\n",
"load('https://sage.unex.es/501708/SAGE/simplex2023Auto_MC.sage')\n",
"#load('https://sage.unex.es/501708/SAGE/simplex2023AutoREVISED.sage')\n",
"#load('https://sage.unex.es/501708/SAGE/simplex2023Auto.sage')\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 94,
"metadata": {},
"outputs": [
{
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""
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"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left[1, 2, 3, 4, 5, 6, 7\\right]$$"
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"text/plain": [
"[1, 2, 3, 4, 5, 6, 7]"
]
},
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},
{
"data": {
"text/plain": [
"[9/10, 1/2, 1/5]"
]
},
"execution_count": 94,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"pardec()"
]
},
{
"cell_type": "code",
"execution_count": 95,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
""
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"text/latex": [
"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left[1, 2, 3, 4, 5, 6, 7\\right]$$"
],
"text/plain": [
"[1, 2, 3, 4, 5, 6, 7]"
]
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"output_type": "display_data"
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{
"data": {
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""
],
"text/latex": [
"$$\\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{green}{s}}_{3} & {\\color{green}{s}}_{4} & {b} \\\\\n",
"\\hline\n",
" {x}_{4} & \\frac{35}{24} & 0 & 0 & 1 & \\frac{17}{120} & \\frac{1}{6} & \\frac{19}{240} & 0 & \\frac{59}{10} \\\\\n",
"{x}_{3} & \\frac{47}{24} & 0 & 1 & 0 & \\frac{1}{24} & \\frac{1}{6} & \\frac{11}{48} & 0 & \\frac{13}{2} \\\\\n",
"{x}_{2} & \\frac{3}{4} & 1 & 0 & 0 & \\frac{1}{20} & 0 & \\frac{7}{40} & 0 & \\frac{16}{5} \\\\\n",
"{\\color{green}{s}}_{4} & -\\frac{1}{24} & 0 & 0 & 0 & -\\frac{1}{24} & -\\frac{1}{6} & -\\frac{11}{48} & 1 & -\\frac{1}{2} \\\\\n",
"\\hline\n",
" {Z_{ind}} & -\\frac{1267}{24} & 0 & 0 & 0 & -\\frac{361}{120} & -\\frac{29}{6} & -\\frac{1667}{240} & 0 & \\frac{2197}{10}\n",
"\\end{array}\\right)$$"
],
"text/plain": [
"[ B| x1 x2 x3 x4 s1 s2 s3 s4| rhs]\n",
"[---------+-------------------------------------------------------------------------------+---------]\n",
"[ x4| 35/24 0 0 1 17/120 1/6 19/240 0| 59/10]\n",
"[ x3| 47/24 0 1 0 1/24 1/6 11/48 0| 13/2]\n",
"[ x2| 3/4 1 0 0 1/20 0 7/40 0| 16/5]\n",
"[ s4| -1/24 0 0 0 -1/24 -1/6 -11/48 1| -1/2]\n",
"[---------+-------------------------------------------------------------------------------+---------]\n",
"[ Z| -1267/24 0 0 0 -361/120 -29/6 -1667/240 0| 2197/10]"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"corte(2) # 1"
]
},
{
"cell_type": "code",
"execution_count": 96,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[1267.0 NO NO NO 72.200 29.000 30.309 NO]"
]
},
"execution_count": 96,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"cocientesD(4)"
]
},
{
"cell_type": "code",
"execution_count": 97,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
""
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"text/latex": [
"$$\\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{green}{s}}_{3} & {\\color{green}{s}}_{4} & {b} \\\\\n",
"\\hline\n",
" {x}_{4} & \\frac{17}{12} & 0 & 0 & 1 & \\frac{1}{10} & 0 & -\\frac{3}{20} & 1 & \\frac{27}{5} \\\\\n",
"{x}_{3} & \\frac{23}{12} & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 6 \\\\\n",
"{x}_{2} & \\frac{3}{4} & 1 & 0 & 0 & \\frac{1}{20} & 0 & \\frac{7}{40} & 0 & \\frac{16}{5} \\\\\n",
"{\\color{green}{s}}_{2} & \\frac{1}{4} & 0 & 0 & 0 & \\frac{1}{4} & 1 & \\frac{11}{8} & -6 & 3 \\\\\n",
"\\hline\n",
" {Z_{ind}} & -\\frac{619}{12} & 0 & 0 & 0 & -\\frac{9}{5} & 0 & -\\frac{3}{10} & -29 & \\frac{1026}{5}\n",
"\\end{array}\\right)$$"
],
"text/plain": [
"[ B| x1 x2 x3 x4 s1 s2 s3 s4| rhs]\n",
"[-------+---------------------------------------------------------------+-------]\n",
"[ x4| 17/12 0 0 1 1/10 0 -3/20 1| 27/5]\n",
"[ x3| 23/12 0 1 0 0 0 0 1| 6]\n",
"[ x2| 3/4 1 0 0 1/20 0 7/40 0| 16/5]\n",
"[ s2| 1/4 0 0 0 1/4 1 11/8 -6| 3]\n",
"[-------+---------------------------------------------------------------+-------]\n",
"[ Z|-619/12 0 0 0 -9/5 0 -3/10 -29| 1026/5]"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"cambio(4,6)"
]
},
{
"cell_type": "code",
"execution_count": 98,
"metadata": {},
"outputs": [
{
"data": {
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""
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"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left[1, 2, 3, 4, 5, 6, 7\\right]$$"
],
"text/plain": [
"[1, 2, 3, 4, 5, 6, 7]"
]
},
"metadata": {},
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},
{
"data": {
"text/plain": [
"[2/5, 0, 1/5, 0]"
]
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"execution_count": 98,
"metadata": {},
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"source": [
"pardec()"
]
},
{
"cell_type": "code",
"execution_count": 99,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
""
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"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left[1, 2, 3, 4, 5, 6, 7\\right]$$"
],
"text/plain": [
"[1, 2, 3, 4, 5, 6, 7]"
]
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"metadata": {},
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{
"data": {
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""
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"text/latex": [
"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrr|r}\n",
"{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\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{17}{12} & 0 & 0 & 1 & \\frac{1}{10} & 0 & -\\frac{3}{20} & 1 & 0 & \\frac{27}{5} \\\\\n",
"{x}_{3} & \\frac{23}{12} & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 6 \\\\\n",
"{x}_{2} & \\frac{3}{4} & 1 & 0 & 0 & \\frac{1}{20} & 0 & \\frac{7}{40} & 0 & 0 & \\frac{16}{5} \\\\\n",
"{\\color{green}{s}}_{2} & \\frac{1}{4} & 0 & 0 & 0 & \\frac{1}{4} & 1 & \\frac{11}{8} & -6 & 0 & 3 \\\\\n",
"{\\color{green}{s}}_{5} & -\\frac{1}{16} & 0 & 0 & 0 & -\\frac{1}{20} & 0 & -\\frac{7}{40} & 0 & 1 & -\\frac{1}{5} \\\\\n",
"\\hline\n",
" {Z_{ind}} & -\\frac{619}{12} & 0 & 0 & 0 & -\\frac{9}{5} & 0 & -\\frac{3}{10} & -29 & 0 & \\frac{1026}{5}\n",
"\\end{array}\\right)$$"
],
"text/plain": [
"[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5| rhs]\n",
"[-------+-----------------------------------------------------------------------+-------]\n",
"[ x4| 17/12 0 0 1 1/10 0 -3/20 1 0| 27/5]\n",
"[ x3| 23/12 0 1 0 0 0 0 1 0| 6]\n",
"[ x2| 3/4 1 0 0 1/20 0 7/40 0 0| 16/5]\n",
"[ s2| 1/4 0 0 0 1/4 1 11/8 -6 0| 3]\n",
"[ s5| -1/16 0 0 0 -1/20 0 -7/40 0 1| -1/5]\n",
"[-------+-----------------------------------------------------------------------+-------]\n",
"[ Z|-619/12 0 0 0 -9/5 0 -3/10 -29 0| 1026/5]"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"corte(3)"
]
},
{
"cell_type": "code",
"execution_count": 100,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[825.33 NO NO NO 36.000 NO 1.7143 NO NO]"
]
},
"execution_count": 100,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"cocientesD(5)"
]
},
{
"cell_type": "code",
"execution_count": 101,
"metadata": {},
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"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrr|r}\n",
"{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {b} \\\\\n",
"\\hline\n",
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"{x}_{3} & \\frac{23}{12} & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 6 \\\\\n",
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"{\\color{green}{s}}_{3} & \\frac{5}{14} & 0 & 0 & 0 & \\frac{2}{7} & 0 & 1 & 0 & -\\frac{40}{7} & \\frac{8}{7} \\\\\n",
"\\hline\n",
" {Z_{ind}} & -\\frac{1081}{21} & 0 & 0 & 0 & -\\frac{12}{7} & 0 & 0 & -29 & -\\frac{12}{7} & \\frac{1434}{7}\n",
"\\end{array}\\right)$$"
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"[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5| rhs]\n",
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"[ x3| 23/12 0 1 0 0 0 0 1 0| 6]\n",
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"[ s2| -27/112 0 0 0 -1/7 1 0 -6 55/7| 10/7]\n",
"[ s3| 5/14 0 0 0 2/7 0 1 0 -40/7| 8/7]\n",
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"[ Z|-1081/21 0 0 0 -12/7 0 0 -29 -12/7| 1434/7]"
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"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrr|r}\n",
"{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {b} \\\\\n",
"\\hline\n",
" {x}_{4} & \\frac{247}{168} & 0 & 0 & 1 & \\frac{1}{7} & 0 & 0 & 1 & -\\frac{6}{7} & 0 & \\frac{39}{7} \\\\\n",
"{x}_{3} & \\frac{23}{12} & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 6 \\\\\n",
"{x}_{2} & \\frac{11}{16} & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 3 \\\\\n",
"{\\color{green}{s}}_{2} & -\\frac{27}{112} & 0 & 0 & 0 & -\\frac{1}{7} & 1 & 0 & -6 & \\frac{55}{7} & 0 & \\frac{10}{7} \\\\\n",
"{\\color{green}{s}}_{3} & \\frac{5}{14} & 0 & 0 & 0 & \\frac{2}{7} & 0 & 1 & 0 & -\\frac{40}{7} & 0 & \\frac{8}{7} \\\\\n",
"{\\color{green}{s}}_{6} & -\\frac{79}{168} & 0 & 0 & 0 & -\\frac{1}{7} & 0 & 0 & -1 & -\\frac{8}{7} & 1 & -\\frac{4}{7} \\\\\n",
"\\hline\n",
" {Z_{ind}} & -\\frac{1081}{21} & 0 & 0 & 0 & -\\frac{12}{7} & 0 & 0 & -29 & -\\frac{12}{7} & 0 & \\frac{1434}{7}\n",
"\\end{array}\\right)$$"
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"[--------+-----------------------------------------------------------------------------------------+--------]\n",
"[ x4| 247/168 0 0 1 1/7 0 0 1 -6/7 0| 39/7]\n",
"[ x3| 23/12 0 1 0 0 0 0 1 0 0| 6]\n",
"[ x2| 11/16 1 0 0 0 0 0 0 1 0| 3]\n",
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"[ s3| 5/14 0 0 0 2/7 0 1 0 -40/7 0| 8/7]\n",
"[ s6| -79/168 0 0 0 -1/7 0 0 -1 -8/7 1| -4/7]\n",
"[--------+-----------------------------------------------------------------------------------------+--------]\n",
"[ Z|-1081/21 0 0 0 -12/7 0 0 -29 -12/7 0| 1434/7]"
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"cell_type": "code",
"execution_count": 105,
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"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrr|r}\n",
"{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {b} \\\\\n",
"\\hline\n",
" {x}_{4} & \\frac{175}{96} & 0 & 0 & 1 & \\frac{1}{4} & 0 & 0 & \\frac{7}{4} & 0 & -\\frac{3}{4} & 6 \\\\\n",
"{x}_{3} & \\frac{23}{12} & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 6 \\\\\n",
"{x}_{2} & \\frac{53}{192} & 1 & 0 & 0 & -\\frac{1}{8} & 0 & 0 & -\\frac{7}{8} & 0 & \\frac{7}{8} & \\frac{5}{2} \\\\\n",
"{\\color{green}{s}}_{2} & -\\frac{667}{192} & 0 & 0 & 0 & -\\frac{9}{8} & 1 & 0 & -\\frac{103}{8} & 0 & \\frac{55}{8} & -\\frac{5}{2} \\\\\n",
"{\\color{green}{s}}_{3} & \\frac{65}{24} & 0 & 0 & 0 & 1 & 0 & 1 & 5 & 0 & -5 & 4 \\\\\n",
"{\\color{green}{s}}_{5} & \\frac{79}{192} & 0 & 0 & 0 & \\frac{1}{8} & 0 & 0 & \\frac{7}{8} & 1 & -\\frac{7}{8} & \\frac{1}{2} \\\\\n",
"\\hline\n",
" {Z_{ind}} & -\\frac{2437}{48} & 0 & 0 & 0 & -\\frac{3}{2} & 0 & 0 & -\\frac{55}{2} & 0 & -\\frac{3}{2} & 204\n",
"\\end{array}\\right)$$"
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"[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6| rhs]\n",
"[--------+-----------------------------------------------------------------------------------------+--------]\n",
"[ x4| 175/96 0 0 1 1/4 0 0 7/4 0 -3/4| 6]\n",
"[ x3| 23/12 0 1 0 0 0 0 1 0 0| 6]\n",
"[ x2| 53/192 1 0 0 -1/8 0 0 -7/8 0 7/8| 5/2]\n",
"[ s2|-667/192 0 0 0 -9/8 1 0 -103/8 0 55/8| -5/2]\n",
"[ s3| 65/24 0 0 0 1 0 1 5 0 -5| 4]\n",
"[ s5| 79/192 0 0 0 1/8 0 0 7/8 1 -7/8| 1/2]\n",
"[--------+-----------------------------------------------------------------------------------------+--------]\n",
"[ Z|-2437/48 0 0 0 -3/2 0 0 -55/2 0 -3/2| 204]"
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"execution_count": 107,
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"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrr|r}\n",
"{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {b} \\\\\n",
"\\hline\n",
" {x}_{4} & \\frac{227}{216} & 0 & 0 & 1 & 0 & \\frac{2}{9} & 0 & -\\frac{10}{9} & 0 & \\frac{7}{9} & \\frac{49}{9} \\\\\n",
"{x}_{3} & \\frac{23}{12} & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 6 \\\\\n",
"{x}_{2} & \\frac{143}{216} & 1 & 0 & 0 & 0 & -\\frac{1}{9} & 0 & \\frac{5}{9} & 0 & \\frac{1}{9} & \\frac{25}{9} \\\\\n",
"{\\color{green}{s}}_{1} & \\frac{667}{216} & 0 & 0 & 0 & 1 & -\\frac{8}{9} & 0 & \\frac{103}{9} & 0 & -\\frac{55}{9} & \\frac{20}{9} \\\\\n",
"{\\color{green}{s}}_{3} & -\\frac{41}{108} & 0 & 0 & 0 & 0 & \\frac{8}{9} & 1 & -\\frac{58}{9} & 0 & \\frac{10}{9} & \\frac{16}{9} \\\\\n",
"{\\color{green}{s}}_{5} & \\frac{11}{432} & 0 & 0 & 0 & 0 & \\frac{1}{9} & 0 & -\\frac{5}{9} & 1 & -\\frac{1}{9} & \\frac{2}{9} \\\\\n",
"\\hline\n",
" {Z_{ind}} & -\\frac{1661}{36} & 0 & 0 & 0 & 0 & -\\frac{4}{3} & 0 & -\\frac{31}{3} & 0 & -\\frac{32}{3} & \\frac{602}{3}\n",
"\\end{array}\\right)$$"
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"[ x3| 23/12 0 1 0 0 0 0 1 0 0| 6]\n",
"[ x2| 143/216 1 0 0 0 -1/9 0 5/9 0 1/9| 25/9]\n",
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"[ s3| -41/108 0 0 0 0 8/9 1 -58/9 0 10/9| 16/9]\n",
"[ s5| 11/432 0 0 0 0 1/9 0 -5/9 1 -1/9| 2/9]\n",
"[--------+-----------------------------------------------------------------------------------------+--------]\n",
"[ Z|-1661/36 0 0 0 0 -4/3 0 -31/3 0 -32/3| 602/3]"
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"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrr|r}\n",
"{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {\\color{green}{s}}_{7} & {b} \\\\\n",
"\\hline\n",
" {x}_{4} & \\frac{227}{216} & 0 & 0 & 1 & 0 & \\frac{2}{9} & 0 & -\\frac{10}{9} & 0 & \\frac{7}{9} & 0 & \\frac{49}{9} \\\\\n",
"{x}_{3} & \\frac{23}{12} & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 6 \\\\\n",
"{x}_{2} & \\frac{143}{216} & 1 & 0 & 0 & 0 & -\\frac{1}{9} & 0 & \\frac{5}{9} & 0 & \\frac{1}{9} & 0 & \\frac{25}{9} \\\\\n",
"{\\color{green}{s}}_{1} & \\frac{667}{216} & 0 & 0 & 0 & 1 & -\\frac{8}{9} & 0 & \\frac{103}{9} & 0 & -\\frac{55}{9} & 0 & \\frac{20}{9} \\\\\n",
"{\\color{green}{s}}_{3} & -\\frac{41}{108} & 0 & 0 & 0 & 0 & \\frac{8}{9} & 1 & -\\frac{58}{9} & 0 & \\frac{10}{9} & 0 & \\frac{16}{9} \\\\\n",
"{\\color{green}{s}}_{5} & \\frac{11}{432} & 0 & 0 & 0 & 0 & \\frac{1}{9} & 0 & -\\frac{5}{9} & 1 & -\\frac{1}{9} & 0 & \\frac{2}{9} \\\\\n",
"{\\color{green}{s}}_{7} & -\\frac{11}{216} & 0 & 0 & 0 & 0 & -\\frac{2}{9} & 0 & -\\frac{8}{9} & 0 & -\\frac{7}{9} & 1 & -\\frac{4}{9} \\\\\n",
"\\hline\n",
" {Z_{ind}} & -\\frac{1661}{36} & 0 & 0 & 0 & 0 & -\\frac{4}{3} & 0 & -\\frac{31}{3} & 0 & -\\frac{32}{3} & 0 & \\frac{602}{3}\n",
"\\end{array}\\right)$$"
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"[--------+--------------------------------------------------------------------------------------------------+--------]\n",
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"[ x3| 23/12 0 1 0 0 0 0 1 0 0 0| 6]\n",
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"[ s7| -11/216 0 0 0 0 -2/9 0 -8/9 0 -7/9 1| -4/9]\n",
"[--------+--------------------------------------------------------------------------------------------------+--------]\n",
"[ Z|-1661/36 0 0 0 0 -4/3 0 -31/3 0 -32/3 0| 602/3]"
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"{\\color{green}{s}}_{3} & -\\frac{7}{12} & 0 & 0 & 0 & 0 & 0 & 1 & -10 & 0 & -2 & 4 & 0 \\\\\n",
"{\\color{green}{s}}_{5} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 1 & -\\frac{1}{2} & \\frac{1}{2} & 0 \\\\\n",
"{\\color{green}{s}}_{2} & \\frac{11}{48} & 0 & 0 & 0 & 0 & 1 & 0 & 4 & 0 & \\frac{7}{2} & -\\frac{9}{2} & 2 \\\\\n",
"\\hline\n",
" {Z_{ind}} & -\\frac{275}{6} & 0 & 0 & 0 & 0 & 0 & 0 & -5 & 0 & -6 & -6 & 198\n",
"\\end{array}\\right)$$"
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"[ Z|-275/6 0 0 0 0 0 0 -5 0 -6 -6| 198]"
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