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"\\begin{array}{lcrcrcrcrcrcrcrcl}\n",
" \\min \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} 48 y_{1} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 100 y_{2} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 70 y_{3} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 64 y_{4} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 150 y_{5} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 90 y_{6} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\\\\n",
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"y_{1}, y_{2}, y_{3}, y_{4}, y_{5}, y_{6}, y_{7} \\geq 0\n",
"\\end{array}$$"
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"$$\\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",
" {\\color{green}{s}}_{1} & 3 & 5 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 48 \\\\\n",
"{\\color{green}{s}}_{2} & 6 & 8 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 100 \\\\\n",
"{\\color{green}{s}}_{3} & 4 & 3 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 70 \\\\\n",
"{\\color{green}{s}}_{4} & 0 & 0 & 2 & 4 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 64 \\\\\n",
"{\\color{green}{s}}_{5} & 0 & 0 & 5 & 9 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 150 \\\\\n",
"{\\color{green}{s}}_{6} & 0 & 0 & 5 & 3 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 90 \\\\\n",
"{\\color{green}{s}}_{7} & -2 & 1 & -2 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 \\\\\n",
"\\hline\n",
" {Z_{ind}} & 44 & 53 & 40 & 34 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\n",
"\\end{array}\\right)$$"
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"[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6 s7|rhs]\n",
"[---+-------------------------------------------+---]\n",
"[ s1| 3 5 0 0 1 0 0 0 0 0 0| 48]\n",
"[ s2| 6 8 0 0 0 1 0 0 0 0 0|100]\n",
"[ s3| 4 3 0 0 0 0 1 0 0 0 0| 70]\n",
"[ s4| 0 0 2 4 0 0 0 1 0 0 0| 64]\n",
"[ s5| 0 0 5 9 0 0 0 0 1 0 0|150]\n",
"[ s6| 0 0 5 3 0 0 0 0 0 1 0| 90]\n",
"[ s7| -2 1 -2 1 0 0 0 0 0 0 1| 0]\n",
"[---+-------------------------------------------+---]\n",
"[ Z| 44 53 40 34 0 0 0 0 0 0 0| 0]"
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"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrr|r}\n",
"{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\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",
" {\\color{green}{s}}_{1} & 13 & 0 & 10 & -5 & 1 & 0 & 0 & 0 & 0 & 0 & -5 & 48 \\\\\n",
"{\\color{green}{s}}_{2} & 22 & 0 & 16 & -8 & 0 & 1 & 0 & 0 & 0 & 0 & -8 & 100 \\\\\n",
"{\\color{green}{s}}_{3} & 10 & 0 & 6 & -3 & 0 & 0 & 1 & 0 & 0 & 0 & -3 & 70 \\\\\n",
"{\\color{green}{s}}_{4} & 0 & 0 & 2 & 4 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 64 \\\\\n",
"{\\color{green}{s}}_{5} & 0 & 0 & 5 & 9 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 150 \\\\\n",
"{\\color{green}{s}}_{6} & 0 & 0 & 5 & 3 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 90 \\\\\n",
"{x}_{2} & -2 & 1 & -2 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 \\\\\n",
"\\hline\n",
" {Z_{ind}} & 150 & 0 & 146 & -19 & 0 & 0 & 0 & 0 & 0 & 0 & -53 & 0\n",
"\\end{array}\\right)$$"
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"[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6 s7|rhs]\n",
"[---+-------------------------------------------+---]\n",
"[ s1| 13 0 10 -5 1 0 0 0 0 0 -5| 48]\n",
"[ s2| 22 0 16 -8 0 1 0 0 0 0 -8|100]\n",
"[ s3| 10 0 6 -3 0 0 1 0 0 0 -3| 70]\n",
"[ s4| 0 0 2 4 0 0 0 1 0 0 0| 64]\n",
"[ s5| 0 0 5 9 0 0 0 0 1 0 0|150]\n",
"[ s6| 0 0 5 3 0 0 0 0 0 1 0| 90]\n",
"[ x2| -2 1 -2 1 0 0 0 0 0 0 1| 0]\n",
"[---+-------------------------------------------+---]\n",
"[ Z|150 0 146 -19 0 0 0 0 0 0 -53| 0]"
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"cambio( 1 , 1 )\n"
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"$$\\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}_{1} & 1 & 0 & \\frac{10}{13} & -\\frac{5}{13} & \\frac{1}{13} & 0 & 0 & 0 & 0 & 0 & -\\frac{5}{13} & \\frac{48}{13} \\\\\n",
"{\\color{green}{s}}_{2} & 0 & 0 & -\\frac{12}{13} & \\frac{6}{13} & -\\frac{22}{13} & 1 & 0 & 0 & 0 & 0 & \\frac{6}{13} & \\frac{244}{13} \\\\\n",
"{\\color{green}{s}}_{3} & 0 & 0 & -\\frac{22}{13} & \\frac{11}{13} & -\\frac{10}{13} & 0 & 1 & 0 & 0 & 0 & \\frac{11}{13} & \\frac{430}{13} \\\\\n",
"{\\color{green}{s}}_{4} & 0 & 0 & 2 & 4 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 64 \\\\\n",
"{\\color{green}{s}}_{5} & 0 & 0 & 5 & 9 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 150 \\\\\n",
"{\\color{green}{s}}_{6} & 0 & 0 & 5 & 3 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 90 \\\\\n",
"{x}_{2} & 0 & 1 & -\\frac{6}{13} & \\frac{3}{13} & \\frac{2}{13} & 0 & 0 & 0 & 0 & 0 & \\frac{3}{13} & \\frac{96}{13} \\\\\n",
"\\hline\n",
" {Z_{ind}} & 0 & 0 & \\frac{398}{13} & \\frac{503}{13} & -\\frac{150}{13} & 0 & 0 & 0 & 0 & 0 & \\frac{61}{13} & \\frac{7200}{13}\n",
"\\end{array}\\right)$$"
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"[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6 s7| rhs]\n",
"[-------+---------------------------------------------------------------------------------------+-------]\n",
"[ x1| 1 0 10/13 -5/13 1/13 0 0 0 0 0 -5/13| 48/13]\n",
"[ s2| 0 0 -12/13 6/13 -22/13 1 0 0 0 0 6/13| 244/13]\n",
"[ s3| 0 0 -22/13 11/13 -10/13 0 1 0 0 0 11/13| 430/13]\n",
"[ s4| 0 0 2 4 0 0 0 1 0 0 0| 64]\n",
"[ s5| 0 0 5 9 0 0 0 0 1 0 0| 150]\n",
"[ s6| 0 0 5 3 0 0 0 0 0 1 0| 90]\n",
"[ x2| 0 1 -6/13 3/13 2/13 0 0 0 0 0 3/13| 96/13]\n",
"[-------+---------------------------------------------------------------------------------------+-------]\n",
"[ Z| 0 0 398/13 503/13 -150/13 0 0 0 0 0 61/13|7200/13]"
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"cambio( 4 , 4 )\n"
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"$$\\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}_{1} & 1 & 0 & \\frac{25}{26} & 0 & \\frac{1}{13} & 0 & 0 & \\frac{5}{52} & 0 & 0 & -\\frac{5}{13} & \\frac{128}{13} \\\\\n",
"{\\color{green}{s}}_{2} & 0 & 0 & -\\frac{15}{13} & 0 & -\\frac{22}{13} & 1 & 0 & -\\frac{3}{26} & 0 & 0 & \\frac{6}{13} & \\frac{148}{13} \\\\\n",
"{\\color{green}{s}}_{3} & 0 & 0 & -\\frac{55}{26} & 0 & -\\frac{10}{13} & 0 & 1 & -\\frac{11}{52} & 0 & 0 & \\frac{11}{13} & \\frac{254}{13} \\\\\n",
"{x}_{4} & 0 & 0 & \\frac{1}{2} & 1 & 0 & 0 & 0 & \\frac{1}{4} & 0 & 0 & 0 & 16 \\\\\n",
"{\\color{green}{s}}_{5} & 0 & 0 & \\frac{1}{2} & 0 & 0 & 0 & 0 & -\\frac{9}{4} & 1 & 0 & 0 & 6 \\\\\n",
"{\\color{green}{s}}_{6} & 0 & 0 & \\frac{7}{2} & 0 & 0 & 0 & 0 & -\\frac{3}{4} & 0 & 1 & 0 & 42 \\\\\n",
"{x}_{2} & 0 & 1 & -\\frac{15}{26} & 0 & \\frac{2}{13} & 0 & 0 & -\\frac{3}{52} & 0 & 0 & \\frac{3}{13} & \\frac{48}{13} \\\\\n",
"\\hline\n",
" {Z_{ind}} & 0 & 0 & \\frac{293}{26} & 0 & -\\frac{150}{13} & 0 & 0 & -\\frac{503}{52} & 0 & 0 & \\frac{61}{13} & \\frac{15248}{13}\n",
"\\end{array}\\right)$$"
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"[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6 s7| rhs]\n",
"[--------+--------------------------------------------------------------------------------------------------+--------]\n",
"[ x1| 1 0 25/26 0 1/13 0 0 5/52 0 0 -5/13| 128/13]\n",
"[ s2| 0 0 -15/13 0 -22/13 1 0 -3/26 0 0 6/13| 148/13]\n",
"[ s3| 0 0 -55/26 0 -10/13 0 1 -11/52 0 0 11/13| 254/13]\n",
"[ x4| 0 0 1/2 1 0 0 0 1/4 0 0 0| 16]\n",
"[ s5| 0 0 1/2 0 0 0 0 -9/4 1 0 0| 6]\n",
"[ s6| 0 0 7/2 0 0 0 0 -3/4 0 1 0| 42]\n",
"[ x2| 0 1 -15/26 0 2/13 0 0 -3/52 0 0 3/13| 48/13]\n",
"[--------+--------------------------------------------------------------------------------------------------+--------]\n",
"[ Z| 0 0 293/26 0 -150/13 0 0 -503/52 0 0 61/13|15248/13]"
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"$$\\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}_{3} & \\frac{26}{25} & 0 & 1 & 0 & \\frac{2}{25} & 0 & 0 & \\frac{1}{10} & 0 & 0 & -\\frac{2}{5} & \\frac{256}{25} \\\\\n",
"{\\color{green}{s}}_{2} & \\frac{6}{5} & 0 & 0 & 0 & -\\frac{8}{5} & 1 & 0 & 0 & 0 & 0 & 0 & \\frac{116}{5} \\\\\n",
"{\\color{green}{s}}_{3} & \\frac{11}{5} & 0 & 0 & 0 & -\\frac{3}{5} & 0 & 1 & 0 & 0 & 0 & 0 & \\frac{206}{5} \\\\\n",
"{x}_{4} & -\\frac{13}{25} & 0 & 0 & 1 & -\\frac{1}{25} & 0 & 0 & \\frac{1}{5} & 0 & 0 & \\frac{1}{5} & \\frac{272}{25} \\\\\n",
"{\\color{green}{s}}_{5} & -\\frac{13}{25} & 0 & 0 & 0 & -\\frac{1}{25} & 0 & 0 & -\\frac{23}{10} & 1 & 0 & \\frac{1}{5} & \\frac{22}{25} \\\\\n",
"{\\color{green}{s}}_{6} & -\\frac{91}{25} & 0 & 0 & 0 & -\\frac{7}{25} & 0 & 0 & -\\frac{11}{10} & 0 & 1 & \\frac{7}{5} & \\frac{154}{25} \\\\\n",
"{x}_{2} & \\frac{3}{5} & 1 & 0 & 0 & \\frac{1}{5} & 0 & 0 & 0 & 0 & 0 & 0 & \\frac{48}{5} \\\\\n",
"\\hline\n",
" {Z_{ind}} & -\\frac{293}{25} & 0 & 0 & 0 & -\\frac{311}{25} & 0 & 0 & -\\frac{54}{5} & 0 & 0 & \\frac{46}{5} & \\frac{32208}{25}\n",
"\\end{array}\\right)$$"
],
"text/plain": [
"[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6 s7| rhs]\n",
"[--------+--------------------------------------------------------------------------------------------------+--------]\n",
"[ x3| 26/25 0 1 0 2/25 0 0 1/10 0 0 -2/5| 256/25]\n",
"[ s2| 6/5 0 0 0 -8/5 1 0 0 0 0 0| 116/5]\n",
"[ s3| 11/5 0 0 0 -3/5 0 1 0 0 0 0| 206/5]\n",
"[ x4| -13/25 0 0 1 -1/25 0 0 1/5 0 0 1/5| 272/25]\n",
"[ s5| -13/25 0 0 0 -1/25 0 0 -23/10 1 0 1/5| 22/25]\n",
"[ s6| -91/25 0 0 0 -7/25 0 0 -11/10 0 1 7/5| 154/25]\n",
"[ x2| 3/5 1 0 0 1/5 0 0 0 0 0 0| 48/5]\n",
"[--------+--------------------------------------------------------------------------------------------------+--------]\n",
"[ Z| -293/25 0 0 0 -311/25 0 0 -54/5 0 0 46/5|32208/25]"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"cambio( 5 , 11 )\n"
]
},
{
"data": {
"text/html": [
""
],
"text/latex": [
"$$\\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}_{3} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & -\\frac{9}{2} & 2 & 0 & 0 & 12 \\\\\n",
"{\\color{green}{s}}_{2} & \\frac{6}{5} & 0 & 0 & 0 & -\\frac{8}{5} & 1 & 0 & 0 & 0 & 0 & 0 & \\frac{116}{5} \\\\\n",
"{\\color{green}{s}}_{3} & \\frac{11}{5} & 0 & 0 & 0 & -\\frac{3}{5} & 0 & 1 & 0 & 0 & 0 & 0 & \\frac{206}{5} \\\\\n",
"{x}_{4} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & \\frac{5}{2} & -1 & 0 & 0 & 10 \\\\\n",
"{\\color{green}{s}}_{7} & -\\frac{13}{5} & 0 & 0 & 0 & -\\frac{1}{5} & 0 & 0 & -\\frac{23}{2} & 5 & 0 & 1 & \\frac{22}{5} \\\\\n",
"{\\color{green}{s}}_{6} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 15 & -7 & 1 & 0 & 0 \\\\\n",
"{x}_{2} & \\frac{3}{5} & 1 & 0 & 0 & \\frac{1}{5} & 0 & 0 & 0 & 0 & 0 & 0 & \\frac{48}{5} \\\\\n",
"\\hline\n",
" {Z_{ind}} & \\frac{61}{5} & 0 & 0 & 0 & -\\frac{53}{5} & 0 & 0 & 95 & -46 & 0 & 0 & \\frac{6644}{5}\n",
"\\end{array}\\right)$$"
],
"text/plain": [
"[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6 s7| rhs]\n",
"[------+----------------------------------------------------------------------------+------]\n",
"[ x3| 0 0 1 0 0 0 0 -9/2 2 0 0| 12]\n",
"[ s2| 6/5 0 0 0 -8/5 1 0 0 0 0 0| 116/5]\n",
"[ s3| 11/5 0 0 0 -3/5 0 1 0 0 0 0| 206/5]\n",
"[ x4| 0 0 0 1 0 0 0 5/2 -1 0 0| 10]\n",
"[ s7| -13/5 0 0 0 -1/5 0 0 -23/2 5 0 1| 22/5]\n",
"[ s6| 0 0 0 0 0 0 0 15 -7 1 0| 0]\n",
"[ x2| 3/5 1 0 0 1/5 0 0 0 0 0 0| 48/5]\n",
"[------+----------------------------------------------------------------------------+------]\n",
"[ Z| 61/5 0 0 0 -53/5 0 0 95 -46 0 0|6644/5]"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"cambio( 6 , 8 )\n"
]
},
{
"data": {
"text/html": [
""
],
"text/latex": [
"$$\\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}_{3} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -\\frac{1}{10} & \\frac{3}{10} & 0 & 12 \\\\\n",
"{\\color{green}{s}}_{2} & \\frac{6}{5} & 0 & 0 & 0 & -\\frac{8}{5} & 1 & 0 & 0 & 0 & 0 & 0 & \\frac{116}{5} \\\\\n",
"{\\color{green}{s}}_{3} & \\frac{11}{5} & 0 & 0 & 0 & -\\frac{3}{5} & 0 & 1 & 0 & 0 & 0 & 0 & \\frac{206}{5} \\\\\n",
"{x}_{4} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & \\frac{1}{6} & -\\frac{1}{6} & 0 & 10 \\\\\n",
"{\\color{green}{s}}_{7} & -\\frac{13}{5} & 0 & 0 & 0 & -\\frac{1}{5} & 0 & 0 & 0 & -\\frac{11}{30} & \\frac{23}{30} & 1 & \\frac{22}{5} \\\\\n",
"{\\color{green}{s}}_{4} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & -\\frac{7}{15} & \\frac{1}{15} & 0 & 0 \\\\\n",
"{x}_{2} & \\frac{3}{5} & 1 & 0 & 0 & \\frac{1}{5} & 0 & 0 & 0 & 0 & 0 & 0 & \\frac{48}{5} \\\\\n",
"\\hline\n",
" {Z_{ind}} & \\frac{61}{5} & 0 & 0 & 0 & -\\frac{53}{5} & 0 & 0 & 0 & -\\frac{5}{3} & -\\frac{19}{3} & 0 & \\frac{6644}{5}\n",
"\\end{array}\\right)$$"
],
"text/plain": [
"[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6 s7| rhs]\n",
"[------+----------------------------------------------------------------------------+------]\n",
"[ x3| 0 0 1 0 0 0 0 0 -1/10 3/10 0| 12]\n",
"[ s2| 6/5 0 0 0 -8/5 1 0 0 0 0 0| 116/5]\n",
"[ s3| 11/5 0 0 0 -3/5 0 1 0 0 0 0| 206/5]\n",
"[ x4| 0 0 0 1 0 0 0 0 1/6 -1/6 0| 10]\n",
"[ s7| -13/5 0 0 0 -1/5 0 0 0 -11/30 23/30 1| 22/5]\n",
"[ s4| 0 0 0 0 0 0 0 1 -7/15 1/15 0| 0]\n",
"[ x2| 3/5 1 0 0 1/5 0 0 0 0 0 0| 48/5]\n",
"[------+----------------------------------------------------------------------------+------]\n",
"[ Z| 61/5 0 0 0 -53/5 0 0 0 -5/3 -19/3 0|6644/5]"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"cambio( 7 , 1 )\n"
]
},
{
"data": {
"text/html": [
""
],
"text/latex": [
"$$\\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}_{3} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -\\frac{1}{10} & \\frac{3}{10} & 0 & 12 \\\\\n",
"{\\color{green}{s}}_{2} & 0 & -2 & 0 & 0 & -2 & 1 & 0 & 0 & 0 & 0 & 0 & 4 \\\\\n",
"{\\color{green}{s}}_{3} & 0 & -\\frac{11}{3} & 0 & 0 & -\\frac{4}{3} & 0 & 1 & 0 & 0 & 0 & 0 & 6 \\\\\n",
"{x}_{4} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & \\frac{1}{6} & -\\frac{1}{6} & 0 & 10 \\\\\n",
"{\\color{green}{s}}_{7} & 0 & \\frac{13}{3} & 0 & 0 & \\frac{2}{3} & 0 & 0 & 0 & -\\frac{11}{30} & \\frac{23}{30} & 1 & 46 \\\\\n",
"{\\color{green}{s}}_{4} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & -\\frac{7}{15} & \\frac{1}{15} & 0 & 0 \\\\\n",
"{x}_{1} & 1 & \\frac{5}{3} & 0 & 0 & \\frac{1}{3} & 0 & 0 & 0 & 0 & 0 & 0 & 16 \\\\\n",
"\\hline\n",
" {Z_{ind}} & 0 & -\\frac{61}{3} & 0 & 0 & -\\frac{44}{3} & 0 & 0 & 0 & -\\frac{5}{3} & -\\frac{19}{3} & 0 & 1524\n",
"\\end{array}\\right)$$"
],
"text/plain": [
"[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6 s7| rhs]\n",
"[------+----------------------------------------------------------------------------+------]\n",
"[ x3| 0 0 1 0 0 0 0 0 -1/10 3/10 0| 12]\n",
"[ s2| 0 -2 0 0 -2 1 0 0 0 0 0| 4]\n",
"[ s3| 0 -11/3 0 0 -4/3 0 1 0 0 0 0| 6]\n",
"[ x4| 0 0 0 1 0 0 0 0 1/6 -1/6 0| 10]\n",
"[ s7| 0 13/3 0 0 2/3 0 0 0 -11/30 23/30 1| 46]\n",
"[ s4| 0 0 0 0 0 0 0 1 -7/15 1/15 0| 0]\n",
"[ x1| 1 5/3 0 0 1/3 0 0 0 0 0 0| 16]\n",
"[------+----------------------------------------------------------------------------+------]\n",
"[ Z| 0 -61/3 0 0 -44/3 0 0 0 -5/3 -19/3 0| 1524]"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"El problema es óptimo\n"
]
}
],
"source": [
"tipo='max' # max o min\n",
"\n",
"n=4 # número de variables x's\n",
"m=6 # número de restricciones (distintas de las de signo)\n",
"\n",
"A=matrix(QQ,m,n,[ # coeficientes de las variables x's\n",
"[3,5,0,0],\n",
"[6,8,0,0],\n",
"[4,3,0,0],\n",
"[0,0,2,4],\n",
"[0,0,5,9],\n",
"[0,0,5,3]\n",
"])\n",
"\n",
"venta=matrix(QQ,1,n,[400,450,400,450]) # precio de venta\n",
"cMP=matrix(QQ,1,m,[18,23,41,20,24,40] ) # coste de las materias primas\n",
"cf=cMP*A # coste de cada unidad de producto fabricada\n",
"c=venta-cf # vector de costos (beneficio en este caso)\n",
"\n",
"nueva_fila = matrix(QQ, 1, 4, [-2, 1, -2, 1]) \n",
"A=A.stack(nueva_fila)\n",
"\n",
"\n",
"b=matrix(QQ,m,1,[48,100,70,64,150,90]) # vector de la derecha\n",
"nuevob=matrix(QQ,1,1,[0]) \n",
"b=b.stack(nuevob)\n",
"\n",
"h=matrix(ZZ,1,m,[1,1,1,1,1,1]) # variables de holgura: \n",
" # Pon 1 si va sumando, \n",
" # -1 si va restando y \n",
" # 0 si no hay variable de holgura.\n",
"nuevah=matrix(ZZ,1,1,[1])\n",
"h=h.augment(nuevah)\n",
"\n",
" \n",
"m=m+1\n",
"\n",
"#######################################################\n",
"\n",
"load('https://sage.unex.es/501708/simplex2023Auto.sage')\n",
"#load('https://sage.unex.es/501708/simplex2023AutoREVISED.sage')\n",
"#load('https://sage.unex.es/501708/simplex2023CompletamenteManual.sage')\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 41,
"metadata": {},
"outputs": [],
"source": [
"#bp=matrix(QQ,m,1,[1,0,0,0,0,0,0]); param1b(bp)"
]
},
{
"cell_type": "code",
"execution_count": 47,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
""
],
"text/latex": [
"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrr|rr}\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} & {b_1} \\\\\n",
"\\hline\n",
" {x}_{3} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -\\frac{1}{10} & \\frac{3}{10} & 0 & 12 & -\\frac{1}{10} \\\\\n",
"{\\color{green}{s}}_{2} & 0 & -2 & 0 & 0 & -2 & 1 & 0 & 0 & 0 & 0 & 0 & 4 & 0 \\\\\n",
"{\\color{green}{s}}_{3} & 0 & -\\frac{11}{3} & 0 & 0 & -\\frac{4}{3} & 0 & 1 & 0 & 0 & 0 & 0 & 6 & 0 \\\\\n",
"{x}_{4} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & \\frac{1}{6} & -\\frac{1}{6} & 0 & 10 & \\frac{1}{6} \\\\\n",
"{\\color{green}{s}}_{7} & 0 & \\frac{13}{3} & 0 & 0 & \\frac{2}{3} & 0 & 0 & 0 & -\\frac{11}{30} & \\frac{23}{30} & 1 & 46 & -\\frac{11}{30} \\\\\n",
"{\\color{green}{s}}_{4} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & -\\frac{7}{15} & \\frac{1}{15} & 0 & 0 & -\\frac{7}{15} \\\\\n",
"{x}_{1} & 1 & \\frac{5}{3} & 0 & 0 & \\frac{1}{3} & 0 & 0 & 0 & 0 & 0 & 0 & 16 & 0 \\\\\n",
"\\hline\n",
" {Z_{ind}} & 0 & -\\frac{61}{3} & 0 & 0 & -\\frac{44}{3} & 0 & 0 & 0 & -\\frac{5}{3} & -\\frac{19}{3} & 0 & 1524 & \\frac{5}{3}\n",
"\\end{array}\\right)$$"
],
"text/plain": [
"[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6 s7| rhs rhs1]\n",
"[------+----------------------------------------------------------------------------+-------------]\n",
"[ x3| 0 0 1 0 0 0 0 0 -1/10 3/10 0| 12 -1/10]\n",
"[ s2| 0 -2 0 0 -2 1 0 0 0 0 0| 4 0]\n",
"[ s3| 0 -11/3 0 0 -4/3 0 1 0 0 0 0| 6 0]\n",
"[ x4| 0 0 0 1 0 0 0 0 1/6 -1/6 0| 10 1/6]\n",
"[ s7| 0 13/3 0 0 2/3 0 0 0 -11/30 23/30 1| 46 -11/30]\n",
"[ s4| 0 0 0 0 0 0 0 1 -7/15 1/15 0| 0 -7/15]\n",
"[ x1| 1 5/3 0 0 1/3 0 0 0 0 0 0| 16 0]\n",
"[------+----------------------------------------------------------------------------+-------------]\n",
"[ Z| 0 -61/3 0 0 -44/3 0 0 0 -5/3 -19/3 0| 1524 5/3]"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"bp=matrix(QQ,m,1,[0,0,0,0,1,0,0]); param1b(bp)"
]
},
{
"cell_type": "code",
"execution_count": 48,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
""
],
"text/latex": [
"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrr|rr}\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} & {b_1} \\\\\n",
"\\hline\n",
" {x}_{3} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & -\\frac{3}{14} & 0 & \\frac{2}{7} & 0 & 12 & 0 \\\\\n",
"{\\color{green}{s}}_{2} & 0 & -2 & 0 & 0 & -2 & 1 & 0 & 0 & 0 & 0 & 0 & 4 & 0 \\\\\n",
"{\\color{green}{s}}_{3} & 0 & -\\frac{11}{3} & 0 & 0 & -\\frac{4}{3} & 0 & 1 & 0 & 0 & 0 & 0 & 6 & 0 \\\\\n",
"{x}_{4} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & \\frac{5}{14} & 0 & -\\frac{1}{7} & 0 & 10 & 0 \\\\\n",
"{\\color{green}{s}}_{7} & 0 & \\frac{13}{3} & 0 & 0 & \\frac{2}{3} & 0 & 0 & -\\frac{11}{14} & 0 & \\frac{5}{7} & 1 & 46 & 0 \\\\\n",
"{\\color{green}{s}}_{5} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -\\frac{15}{7} & 1 & -\\frac{1}{7} & 0 & 0 & 1 \\\\\n",
"{x}_{1} & 1 & \\frac{5}{3} & 0 & 0 & \\frac{1}{3} & 0 & 0 & 0 & 0 & 0 & 0 & 16 & 0 \\\\\n",
"\\hline\n",
" {Z_{ind}} & 0 & -\\frac{61}{3} & 0 & 0 & -\\frac{44}{3} & 0 & 0 & -\\frac{25}{7} & 0 & -\\frac{46}{7} & 0 & 1524 & 0\n",
"\\end{array}\\right)$$"
],
"text/plain": [
"[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6 s7| rhs rhs1]\n",
"[------+----------------------------------------------------------------------------+-------------]\n",
"[ x3| 0 0 1 0 0 0 0 -3/14 0 2/7 0| 12 0]\n",
"[ s2| 0 -2 0 0 -2 1 0 0 0 0 0| 4 0]\n",
"[ s3| 0 -11/3 0 0 -4/3 0 1 0 0 0 0| 6 0]\n",
"[ x4| 0 0 0 1 0 0 0 5/14 0 -1/7 0| 10 0]\n",
"[ s7| 0 13/3 0 0 2/3 0 0 -11/14 0 5/7 1| 46 0]\n",
"[ s5| 0 0 0 0 0 0 0 -15/7 1 -1/7 0| 0 1]\n",
"[ x1| 1 5/3 0 0 1/3 0 0 0 0 0 0| 16 0]\n",
"[------+----------------------------------------------------------------------------+-------------]\n",
"[ Z| 0 -61/3 0 0 -44/3 0 0 -25/7 0 -46/7 0| 1524 0]"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"cambio(6,9)"
]
},
{
"cell_type": "code",
"execution_count": 44,
"metadata": {},
"outputs": [],
"source": [
"#cambio(6,8)"
]
},
{
"cell_type": "code",
"execution_count": 45,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
""
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"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$$"
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{
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""
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"data": {
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"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{l}\n",
"\\begin{array}{lcrcrcrcrcl}\n",
" \\max \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} 44 x_{1} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 53 x_{2} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 40 x_{3} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 34 x_{4} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\\\\n",
" \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} 3 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} \\mspace{-6mu}&\\mspace{-6mu} \\leq \\mspace{-6mu}&\\mspace{-6mu} 48 \\\\\n",
" \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} 6 x_{1} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 8 x_{2} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\leq \\mspace{-6mu}&\\mspace{-6mu} 100 \\\\\n",
" \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} 4 x_{1} \\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} \\mspace{-6mu}&\\mspace{-6mu} \\leq \\mspace{-6mu}&\\mspace{-6mu} 70 \\\\\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} 2 x_{3} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 4 x_{4} \\mspace{-6mu}&\\mspace{-6mu} \\leq \\mspace{-6mu}&\\mspace{-6mu} 64 \\\\\n",
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"\\end{array}$$"
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"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{l}\n",
"\\begin{array}{lcrcrcrcrcrcrcrcl}\n",
" \\min \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} 48 y_{1} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 100 y_{2} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 70 y_{3} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 64 y_{4} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 150 y_{5} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 90 y_{6} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\\\\n",
" \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} 3 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} \\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} 2 y_{7} \\mspace{-6mu}&\\mspace{-6mu} \\geq \\mspace{-6mu}&\\mspace{-6mu} 44 \\\\\n",
" \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} 5 y_{1} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 8 y_{2} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 3 y_{3} \\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} y_{7} \\mspace{-6mu}&\\mspace{-6mu} \\geq \\mspace{-6mu}&\\mspace{-6mu} 53 \\\\\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} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} 2 y_{4} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 5 y_{5} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 5 y_{6} \\mspace{-6mu}&\\mspace{-6mu} - \\mspace{-6mu}&\\mspace{-6mu} 2 y_{7} \\mspace{-6mu}&\\mspace{-6mu} \\geq \\mspace{-6mu}&\\mspace{-6mu} 40 \\\\\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} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} 4 y_{4} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 9 y_{5} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 3 y_{6} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} y_{7} \\mspace{-6mu}&\\mspace{-6mu} \\geq \\mspace{-6mu}&\\mspace{-6mu} 34 \\\\\n",
"\\end{array} \\\\\n",
"y_{1}, y_{2}, y_{3}, y_{4}, y_{5}, y_{6}, y_{7} \\geq 0\n",
"\\end{array}$$"
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"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\frac{44}{3},\\,0,\\,0,\\,0,\\,\\frac{5}{3},\\,\\frac{19}{3},\\,0\\right)$$"
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"$$\\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",
" {\\color{green}{s}}_{1} & 3 & 5 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 48 \\\\\n",
"{\\color{green}{s}}_{2} & 6 & 8 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 100 \\\\\n",
"{\\color{green}{s}}_{3} & 4 & 3 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 70 \\\\\n",
"{\\color{green}{s}}_{4} & 0 & 0 & 2 & 4 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 64 \\\\\n",
"{\\color{green}{s}}_{5} & 0 & 0 & 5 & 9 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 150 \\\\\n",
"{\\color{green}{s}}_{6} & 0 & 0 & 5 & 3 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 90 \\\\\n",
"{\\color{green}{s}}_{7} & -2 & 1 & -2 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 \\\\\n",
"\\hline\n",
" {Z_{ind}} & 44 & 53 & 40 & 34 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\n",
"\\end{array}\\right)$$"
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"[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6 s7|rhs]\n",
"[---+-------------------------------------------+---]\n",
"[ s1| 3 5 0 0 1 0 0 0 0 0 0| 48]\n",
"[ s2| 6 8 0 0 0 1 0 0 0 0 0|100]\n",
"[ s3| 4 3 0 0 0 0 1 0 0 0 0| 70]\n",
"[ s4| 0 0 2 4 0 0 0 1 0 0 0| 64]\n",
"[ s5| 0 0 5 9 0 0 0 0 1 0 0|150]\n",
"[ s6| 0 0 5 3 0 0 0 0 0 1 0| 90]\n",
"[ s7| -2 1 -2 1 0 0 0 0 0 0 1| 0]\n",
"[---+-------------------------------------------+---]\n",
"[ Z| 44 53 40 34 0 0 0 0 0 0 0| 0]"
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"text": [
"cambio( 7 , 2 )\n"
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"$$\\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",
" {\\color{green}{s}}_{1} & 13 & 0 & 10 & -5 & 1 & 0 & 0 & 0 & 0 & 0 & -5 & 48 \\\\\n",
"{\\color{green}{s}}_{2} & 22 & 0 & 16 & -8 & 0 & 1 & 0 & 0 & 0 & 0 & -8 & 100 \\\\\n",
"{\\color{green}{s}}_{3} & 10 & 0 & 6 & -3 & 0 & 0 & 1 & 0 & 0 & 0 & -3 & 70 \\\\\n",
"{\\color{green}{s}}_{4} & 0 & 0 & 2 & 4 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 64 \\\\\n",
"{\\color{green}{s}}_{5} & 0 & 0 & 5 & 9 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 150 \\\\\n",
"{\\color{green}{s}}_{6} & 0 & 0 & 5 & 3 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 90 \\\\\n",
"{x}_{2} & -2 & 1 & -2 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 \\\\\n",
"\\hline\n",
" {Z_{ind}} & 150 & 0 & 146 & -19 & 0 & 0 & 0 & 0 & 0 & 0 & -53 & 0\n",
"\\end{array}\\right)$$"
],
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"[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6 s7|rhs]\n",
"[---+-------------------------------------------+---]\n",
"[ s1| 13 0 10 -5 1 0 0 0 0 0 -5| 48]\n",
"[ s2| 22 0 16 -8 0 1 0 0 0 0 -8|100]\n",
"[ s3| 10 0 6 -3 0 0 1 0 0 0 -3| 70]\n",
"[ s4| 0 0 2 4 0 0 0 1 0 0 0| 64]\n",
"[ s5| 0 0 5 9 0 0 0 0 1 0 0|150]\n",
"[ s6| 0 0 5 3 0 0 0 0 0 1 0| 90]\n",
"[ x2| -2 1 -2 1 0 0 0 0 0 0 1| 0]\n",
"[---+-------------------------------------------+---]\n",
"[ Z|150 0 146 -19 0 0 0 0 0 0 -53| 0]"
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"text": [
"cambio( 1 , 1 )\n"
]
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"$$\\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}_{1} & 1 & 0 & \\frac{10}{13} & -\\frac{5}{13} & \\frac{1}{13} & 0 & 0 & 0 & 0 & 0 & -\\frac{5}{13} & \\frac{48}{13} \\\\\n",
"{\\color{green}{s}}_{2} & 0 & 0 & -\\frac{12}{13} & \\frac{6}{13} & -\\frac{22}{13} & 1 & 0 & 0 & 0 & 0 & \\frac{6}{13} & \\frac{244}{13} \\\\\n",
"{\\color{green}{s}}_{3} & 0 & 0 & -\\frac{22}{13} & \\frac{11}{13} & -\\frac{10}{13} & 0 & 1 & 0 & 0 & 0 & \\frac{11}{13} & \\frac{430}{13} \\\\\n",
"{\\color{green}{s}}_{4} & 0 & 0 & 2 & 4 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 64 \\\\\n",
"{\\color{green}{s}}_{5} & 0 & 0 & 5 & 9 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 150 \\\\\n",
"{\\color{green}{s}}_{6} & 0 & 0 & 5 & 3 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 90 \\\\\n",
"{x}_{2} & 0 & 1 & -\\frac{6}{13} & \\frac{3}{13} & \\frac{2}{13} & 0 & 0 & 0 & 0 & 0 & \\frac{3}{13} & \\frac{96}{13} \\\\\n",
"\\hline\n",
" {Z_{ind}} & 0 & 0 & \\frac{398}{13} & \\frac{503}{13} & -\\frac{150}{13} & 0 & 0 & 0 & 0 & 0 & \\frac{61}{13} & \\frac{7200}{13}\n",
"\\end{array}\\right)$$"
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"[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6 s7| rhs]\n",
"[-------+---------------------------------------------------------------------------------------+-------]\n",
"[ x1| 1 0 10/13 -5/13 1/13 0 0 0 0 0 -5/13| 48/13]\n",
"[ s2| 0 0 -12/13 6/13 -22/13 1 0 0 0 0 6/13| 244/13]\n",
"[ s3| 0 0 -22/13 11/13 -10/13 0 1 0 0 0 11/13| 430/13]\n",
"[ s4| 0 0 2 4 0 0 0 1 0 0 0| 64]\n",
"[ s5| 0 0 5 9 0 0 0 0 1 0 0| 150]\n",
"[ s6| 0 0 5 3 0 0 0 0 0 1 0| 90]\n",
"[ x2| 0 1 -6/13 3/13 2/13 0 0 0 0 0 3/13| 96/13]\n",
"[-------+---------------------------------------------------------------------------------------+-------]\n",
"[ Z| 0 0 398/13 503/13 -150/13 0 0 0 0 0 61/13|7200/13]"
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"text": [
"cambio( 4 , 4 )\n"
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"$$\\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}_{1} & 1 & 0 & \\frac{25}{26} & 0 & \\frac{1}{13} & 0 & 0 & \\frac{5}{52} & 0 & 0 & -\\frac{5}{13} & \\frac{128}{13} \\\\\n",
"{\\color{green}{s}}_{2} & 0 & 0 & -\\frac{15}{13} & 0 & -\\frac{22}{13} & 1 & 0 & -\\frac{3}{26} & 0 & 0 & \\frac{6}{13} & \\frac{148}{13} \\\\\n",
"{\\color{green}{s}}_{3} & 0 & 0 & -\\frac{55}{26} & 0 & -\\frac{10}{13} & 0 & 1 & -\\frac{11}{52} & 0 & 0 & \\frac{11}{13} & \\frac{254}{13} \\\\\n",
"{x}_{4} & 0 & 0 & \\frac{1}{2} & 1 & 0 & 0 & 0 & \\frac{1}{4} & 0 & 0 & 0 & 16 \\\\\n",
"{\\color{green}{s}}_{5} & 0 & 0 & \\frac{1}{2} & 0 & 0 & 0 & 0 & -\\frac{9}{4} & 1 & 0 & 0 & 6 \\\\\n",
"{\\color{green}{s}}_{6} & 0 & 0 & \\frac{7}{2} & 0 & 0 & 0 & 0 & -\\frac{3}{4} & 0 & 1 & 0 & 42 \\\\\n",
"{x}_{2} & 0 & 1 & -\\frac{15}{26} & 0 & \\frac{2}{13} & 0 & 0 & -\\frac{3}{52} & 0 & 0 & \\frac{3}{13} & \\frac{48}{13} \\\\\n",
"\\hline\n",
" {Z_{ind}} & 0 & 0 & \\frac{293}{26} & 0 & -\\frac{150}{13} & 0 & 0 & -\\frac{503}{52} & 0 & 0 & \\frac{61}{13} & \\frac{15248}{13}\n",
"\\end{array}\\right)$$"
],
"text/plain": [
"[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6 s7| rhs]\n",
"[--------+--------------------------------------------------------------------------------------------------+--------]\n",
"[ x1| 1 0 25/26 0 1/13 0 0 5/52 0 0 -5/13| 128/13]\n",
"[ s2| 0 0 -15/13 0 -22/13 1 0 -3/26 0 0 6/13| 148/13]\n",
"[ s3| 0 0 -55/26 0 -10/13 0 1 -11/52 0 0 11/13| 254/13]\n",
"[ x4| 0 0 1/2 1 0 0 0 1/4 0 0 0| 16]\n",
"[ s5| 0 0 1/2 0 0 0 0 -9/4 1 0 0| 6]\n",
"[ s6| 0 0 7/2 0 0 0 0 -3/4 0 1 0| 42]\n",
"[ x2| 0 1 -15/26 0 2/13 0 0 -3/52 0 0 3/13| 48/13]\n",
"[--------+--------------------------------------------------------------------------------------------------+--------]\n",
"[ Z| 0 0 293/26 0 -150/13 0 0 -503/52 0 0 61/13|15248/13]"
]
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"text": [
"cambio( 1 , 3 )\n"
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"$$\\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}_{3} & \\frac{26}{25} & 0 & 1 & 0 & \\frac{2}{25} & 0 & 0 & \\frac{1}{10} & 0 & 0 & -\\frac{2}{5} & \\frac{256}{25} \\\\\n",
"{\\color{green}{s}}_{2} & \\frac{6}{5} & 0 & 0 & 0 & -\\frac{8}{5} & 1 & 0 & 0 & 0 & 0 & 0 & \\frac{116}{5} \\\\\n",
"{\\color{green}{s}}_{3} & \\frac{11}{5} & 0 & 0 & 0 & -\\frac{3}{5} & 0 & 1 & 0 & 0 & 0 & 0 & \\frac{206}{5} \\\\\n",
"{x}_{4} & -\\frac{13}{25} & 0 & 0 & 1 & -\\frac{1}{25} & 0 & 0 & \\frac{1}{5} & 0 & 0 & \\frac{1}{5} & \\frac{272}{25} \\\\\n",
"{\\color{green}{s}}_{5} & -\\frac{13}{25} & 0 & 0 & 0 & -\\frac{1}{25} & 0 & 0 & -\\frac{23}{10} & 1 & 0 & \\frac{1}{5} & \\frac{22}{25} \\\\\n",
"{\\color{green}{s}}_{6} & -\\frac{91}{25} & 0 & 0 & 0 & -\\frac{7}{25} & 0 & 0 & -\\frac{11}{10} & 0 & 1 & \\frac{7}{5} & \\frac{154}{25} \\\\\n",
"{x}_{2} & \\frac{3}{5} & 1 & 0 & 0 & \\frac{1}{5} & 0 & 0 & 0 & 0 & 0 & 0 & \\frac{48}{5} \\\\\n",
"\\hline\n",
" {Z_{ind}} & -\\frac{293}{25} & 0 & 0 & 0 & -\\frac{311}{25} & 0 & 0 & -\\frac{54}{5} & 0 & 0 & \\frac{46}{5} & \\frac{32208}{25}\n",
"\\end{array}\\right)$$"
],
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"[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6 s7| rhs]\n",
"[--------+--------------------------------------------------------------------------------------------------+--------]\n",
"[ x3| 26/25 0 1 0 2/25 0 0 1/10 0 0 -2/5| 256/25]\n",
"[ s2| 6/5 0 0 0 -8/5 1 0 0 0 0 0| 116/5]\n",
"[ s3| 11/5 0 0 0 -3/5 0 1 0 0 0 0| 206/5]\n",
"[ x4| -13/25 0 0 1 -1/25 0 0 1/5 0 0 1/5| 272/25]\n",
"[ s5| -13/25 0 0 0 -1/25 0 0 -23/10 1 0 1/5| 22/25]\n",
"[ s6| -91/25 0 0 0 -7/25 0 0 -11/10 0 1 7/5| 154/25]\n",
"[ x2| 3/5 1 0 0 1/5 0 0 0 0 0 0| 48/5]\n",
"[--------+--------------------------------------------------------------------------------------------------+--------]\n",
"[ Z| -293/25 0 0 0 -311/25 0 0 -54/5 0 0 46/5|32208/25]"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"cambio( 5 , 11 )\n"
]
},
{
"data": {
"text/html": [
""
],
"text/latex": [
"$$\\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}_{3} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & -\\frac{9}{2} & 2 & 0 & 0 & 12 \\\\\n",
"{\\color{green}{s}}_{2} & \\frac{6}{5} & 0 & 0 & 0 & -\\frac{8}{5} & 1 & 0 & 0 & 0 & 0 & 0 & \\frac{116}{5} \\\\\n",
"{\\color{green}{s}}_{3} & \\frac{11}{5} & 0 & 0 & 0 & -\\frac{3}{5} & 0 & 1 & 0 & 0 & 0 & 0 & \\frac{206}{5} \\\\\n",
"{x}_{4} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & \\frac{5}{2} & -1 & 0 & 0 & 10 \\\\\n",
"{\\color{green}{s}}_{7} & -\\frac{13}{5} & 0 & 0 & 0 & -\\frac{1}{5} & 0 & 0 & -\\frac{23}{2} & 5 & 0 & 1 & \\frac{22}{5} \\\\\n",
"{\\color{green}{s}}_{6} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 15 & -7 & 1 & 0 & 0 \\\\\n",
"{x}_{2} & \\frac{3}{5} & 1 & 0 & 0 & \\frac{1}{5} & 0 & 0 & 0 & 0 & 0 & 0 & \\frac{48}{5} \\\\\n",
"\\hline\n",
" {Z_{ind}} & \\frac{61}{5} & 0 & 0 & 0 & -\\frac{53}{5} & 0 & 0 & 95 & -46 & 0 & 0 & \\frac{6644}{5}\n",
"\\end{array}\\right)$$"
],
"text/plain": [
"[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6 s7| rhs]\n",
"[------+----------------------------------------------------------------------------+------]\n",
"[ x3| 0 0 1 0 0 0 0 -9/2 2 0 0| 12]\n",
"[ s2| 6/5 0 0 0 -8/5 1 0 0 0 0 0| 116/5]\n",
"[ s3| 11/5 0 0 0 -3/5 0 1 0 0 0 0| 206/5]\n",
"[ x4| 0 0 0 1 0 0 0 5/2 -1 0 0| 10]\n",
"[ s7| -13/5 0 0 0 -1/5 0 0 -23/2 5 0 1| 22/5]\n",
"[ s6| 0 0 0 0 0 0 0 15 -7 1 0| 0]\n",
"[ x2| 3/5 1 0 0 1/5 0 0 0 0 0 0| 48/5]\n",
"[------+----------------------------------------------------------------------------+------]\n",
"[ Z| 61/5 0 0 0 -53/5 0 0 95 -46 0 0|6644/5]"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"cambio( 6 , 8 )\n"
]
},
{
"data": {
"text/html": [
""
],
"text/latex": [
"$$\\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}_{3} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -\\frac{1}{10} & \\frac{3}{10} & 0 & 12 \\\\\n",
"{\\color{green}{s}}_{2} & \\frac{6}{5} & 0 & 0 & 0 & -\\frac{8}{5} & 1 & 0 & 0 & 0 & 0 & 0 & \\frac{116}{5} \\\\\n",
"{\\color{green}{s}}_{3} & \\frac{11}{5} & 0 & 0 & 0 & -\\frac{3}{5} & 0 & 1 & 0 & 0 & 0 & 0 & \\frac{206}{5} \\\\\n",
"{x}_{4} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & \\frac{1}{6} & -\\frac{1}{6} & 0 & 10 \\\\\n",
"{\\color{green}{s}}_{7} & -\\frac{13}{5} & 0 & 0 & 0 & -\\frac{1}{5} & 0 & 0 & 0 & -\\frac{11}{30} & \\frac{23}{30} & 1 & \\frac{22}{5} \\\\\n",
"{\\color{green}{s}}_{4} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & -\\frac{7}{15} & \\frac{1}{15} & 0 & 0 \\\\\n",
"{x}_{2} & \\frac{3}{5} & 1 & 0 & 0 & \\frac{1}{5} & 0 & 0 & 0 & 0 & 0 & 0 & \\frac{48}{5} \\\\\n",
"\\hline\n",
" {Z_{ind}} & \\frac{61}{5} & 0 & 0 & 0 & -\\frac{53}{5} & 0 & 0 & 0 & -\\frac{5}{3} & -\\frac{19}{3} & 0 & \\frac{6644}{5}\n",
"\\end{array}\\right)$$"
],
"text/plain": [
"[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6 s7| rhs]\n",
"[------+----------------------------------------------------------------------------+------]\n",
"[ x3| 0 0 1 0 0 0 0 0 -1/10 3/10 0| 12]\n",
"[ s2| 6/5 0 0 0 -8/5 1 0 0 0 0 0| 116/5]\n",
"[ s3| 11/5 0 0 0 -3/5 0 1 0 0 0 0| 206/5]\n",
"[ x4| 0 0 0 1 0 0 0 0 1/6 -1/6 0| 10]\n",
"[ s7| -13/5 0 0 0 -1/5 0 0 0 -11/30 23/30 1| 22/5]\n",
"[ s4| 0 0 0 0 0 0 0 1 -7/15 1/15 0| 0]\n",
"[ x2| 3/5 1 0 0 1/5 0 0 0 0 0 0| 48/5]\n",
"[------+----------------------------------------------------------------------------+------]\n",
"[ Z| 61/5 0 0 0 -53/5 0 0 0 -5/3 -19/3 0|6644/5]"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"cambio( 7 , 1 )\n"
]
},
{
"data": {
"text/html": [
""
],
"text/latex": [
"$$\\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}_{3} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -\\frac{1}{10} & \\frac{3}{10} & 0 & 12 \\\\\n",
"{\\color{green}{s}}_{2} & 0 & -2 & 0 & 0 & -2 & 1 & 0 & 0 & 0 & 0 & 0 & 4 \\\\\n",
"{\\color{green}{s}}_{3} & 0 & -\\frac{11}{3} & 0 & 0 & -\\frac{4}{3} & 0 & 1 & 0 & 0 & 0 & 0 & 6 \\\\\n",
"{x}_{4} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & \\frac{1}{6} & -\\frac{1}{6} & 0 & 10 \\\\\n",
"{\\color{green}{s}}_{7} & 0 & \\frac{13}{3} & 0 & 0 & \\frac{2}{3} & 0 & 0 & 0 & -\\frac{11}{30} & \\frac{23}{30} & 1 & 46 \\\\\n",
"{\\color{green}{s}}_{4} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & -\\frac{7}{15} & \\frac{1}{15} & 0 & 0 \\\\\n",
"{x}_{1} & 1 & \\frac{5}{3} & 0 & 0 & \\frac{1}{3} & 0 & 0 & 0 & 0 & 0 & 0 & 16 \\\\\n",
"\\hline\n",
" {Z_{ind}} & 0 & -\\frac{61}{3} & 0 & 0 & -\\frac{44}{3} & 0 & 0 & 0 & -\\frac{5}{3} & -\\frac{19}{3} & 0 & 1524\n",
"\\end{array}\\right)$$"
],
"text/plain": [
"[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6 s7| rhs]\n",
"[------+----------------------------------------------------------------------------+------]\n",
"[ x3| 0 0 1 0 0 0 0 0 -1/10 3/10 0| 12]\n",
"[ s2| 0 -2 0 0 -2 1 0 0 0 0 0| 4]\n",
"[ s3| 0 -11/3 0 0 -4/3 0 1 0 0 0 0| 6]\n",
"[ x4| 0 0 0 1 0 0 0 0 1/6 -1/6 0| 10]\n",
"[ s7| 0 13/3 0 0 2/3 0 0 0 -11/30 23/30 1| 46]\n",
"[ s4| 0 0 0 0 0 0 0 1 -7/15 1/15 0| 0]\n",
"[ x1| 1 5/3 0 0 1/3 0 0 0 0 0 0| 16]\n",
"[------+----------------------------------------------------------------------------+------]\n",
"[ Z| 0 -61/3 0 0 -44/3 0 0 0 -5/3 -19/3 0| 1524]"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"El problema es óptimo\n"
]
}
],
"source": [
"tipo='max' # max o min\n",
"\n",
"n=4 # número de variables x's\n",
"m=6 # número de restricciones (distintas de las de signo)\n",
"\n",
"A=matrix(QQ,m,n,[ # coeficientes de las variables x's\n",
"[3,5,0,0],\n",
"[6,8,0,0],\n",
"[4,3,0,0],\n",
"[0,0,2,4],\n",
"[0,0,5,9],\n",
"[0,0,5,3]\n",
"])\n",
"\n",
"venta=matrix(QQ,1,n,[400,450,400,450]) # precio de venta\n",
"cMP=matrix(QQ,1,m,[18,23,41,20,24,40] ) # coste de las materias primas\n",
"cf=cMP*A # coste de cada unidad de producto fabricada\n",
"c=venta-cf # vector de costos (beneficio en este caso)\n",
"\n",
"nueva_fila = matrix(QQ, 1, 4, [-2, 1, -2, 1]) \n",
"A=A.stack(nueva_fila)\n",
"\n",
"\n",
"b=matrix(QQ,m,1,[48,100,70,64,150,90]) # vector de la derecha\n",
"nuevob=matrix(QQ,1,1,[0]) \n",
"b=b.stack(nuevob)\n",
"\n",
"h=matrix(ZZ,1,m,[1,1,1,1,1,1]) # variables de holgura: \n",
" # Pon 1 si va sumando, \n",
" # -1 si va restando y \n",
" # 0 si no hay variable de holgura.\n",
"nuevah=matrix(ZZ,1,1,[1])\n",
"h=h.augment(nuevah)\n",
"\n",
" \n",
"m=m+1\n",
"\n",
"#######################################################\n",
"\n",
"load('https://sage.unex.es/501708/simplex2023Auto.sage')\n",
"#load('https://sage.unex.es/501708/simplex2023AutoREVISED.sage')\n",
"#load('https://sage.unex.es/501708/simplex2023CompletamenteManual.sage')\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
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