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"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 1 & 6 & -7 & 7 & 1 & 0 & 0 & 20 \\\\\n", "{\\color{green}{s}}_{2} & 6 & -7 & 5 & 1 & 0 & 1 & 0 & 16 \\\\\n", "{\\color{green}{s}}_{3} & 4 & 4 & 2 & -2 & 0 & 0 & 1 & 14 \\\\\n", "\\hline\n", " {Z_{ind}} & 17 & 12 & 7 & 20 & 0 & 0 & 0 & 0\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3|rhs]\n", "[---+---------------------------+---]\n", "[ s1| 1 6 -7 7 1 0 0| 20]\n", "[ s2| 6 -7 5 1 0 1 0| 16]\n", "[ s3| 4 4 2 -2 0 0 1| 14]\n", "[---+---------------------------+---]\n", "[ Z| 17 12 7 20 0 0 0| 0]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ " \n", " \n", "cambio( 1 , 4 )\n", "cambio( 2 , 3 )\n", "cambio( 3 , 2 )\n" ] }, { "data": { 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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,[17,12,7,20] ) # 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,[20,16,14]) # 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", "\n", "#load('https://sage.unex.es/501708/simplex2023Auto.sage')\n", "load('https://sage.unex.es/501708/simplex2023Auto_MC.sage')\n" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {b} \\\\\n", "\\hline\n", " {x}_{4} & \\frac{35}{24} & 0 & 0 & 1 & \\frac{17}{120} & \\frac{1}{6} & \\frac{19}{240} & 0 & \\frac{793}{120} \\\\\n", "{x}_{3} & \\frac{47}{24} & 0 & 1 & 0 & \\frac{1}{24} & \\frac{1}{6} & \\frac{11}{48} & 0 & \\frac{161}{24} \\\\\n", "{x}_{2} & \\frac{3}{4} & 1 & 0 & 0 & \\frac{1}{20} & 0 & \\frac{7}{40} & 0 & \\frac{69}{20} \\\\\n", "{\\color{green}{s}}_{4} & -\\frac{3}{4} & 0 & 0 & 0 & -\\frac{1}{20} & 0 & -\\frac{7}{40} & 1 & -\\frac{9}{20} \\\\\n", "\\hline\n", " {Z_{ind}} & -\\frac{279}{8} & 0 & 0 & 0 & -\\frac{149}{40} & -\\frac{9}{2} & -\\frac{423}{80} & 0 & \\frac{8821}{40}\n", "\\end{array}\\right)$ " ], "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{793}{120} \\\\\n", "{x}_{3} & \\frac{47}{24} & 0 & 1 & 0 & \\frac{1}{24} & \\frac{1}{6} & \\frac{11}{48} & 0 & \\frac{161}{24} \\\\\n", "{x}_{2} & \\frac{3}{4} & 1 & 0 & 0 & \\frac{1}{20} & 0 & \\frac{7}{40} & 0 & \\frac{69}{20} \\\\\n", "{\\color{green}{s}}_{4} & -\\frac{3}{4} & 0 & 0 & 0 & -\\frac{1}{20} & 0 & -\\frac{7}{40} & 1 & -\\frac{9}{20} \\\\\n", "\\hline\n", " {Z_{ind}} & -\\frac{279}{8} & 0 & 0 & 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