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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": 6, "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{9}{44} & 0 & 0 & 0 & -\\frac{1}{20} & 0 & 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\\frac{631}{462} & 0 & 0 & 1 & \\frac{5}{42} & \\frac{1}{6} & 0 & \\frac{19}{42} & 0 & \\frac{269}{42} \\\\\n", "{x}_{3} & \\frac{71}{42} & 0 & 1 & 0 & -\\frac{1}{42} & \\frac{1}{6} & 0 & \\frac{55}{42} & 0 & \\frac{257}{42} \\\\\n", "{x}_{2} & \\frac{6}{11} & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 3 \\\\\n", "{\\color{green}{s}}_{3} & \\frac{90}{77} & 0 & 0 & 0 & \\frac{2}{7} & 0 & 1 & -\\frac{40}{7} & 0 & \\frac{18}{7} \\\\\n", "{\\color{green}{s}}_{5} & -\\frac{65}{1554} & 0 & 0 & 0 & -\\frac{5}{1554} & -\\frac{25}{222} & 0 & -\\frac{55}{42} & 1 & -\\frac{5}{42} \\\\\n", "\\hline\n", " {Z_{ind}} & -\\frac{4419}{154} & 0 & 0 & 0 & -\\frac{31}{14} & -\\frac{9}{2} & 0 & -\\frac{423}{14} & 0 & \\frac{2897}{14}\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5| rhs]\n", "[---------+-----------------------------------------------------------------------------------------+---------]\n", "[ x4| 631/462 0 0 1 5/42 1/6 0 19/42 0| 269/42]\n", "[ x3| 71/42 0 1 0 -1/42 1/6 0 55/42 0| 257/42]\n", "[ x2| 6/11 1 0 0 0 0 0 1 0| 3]\n", "[ s3| 90/77 0 0 0 2/7 0 1 -40/7 0| 18/7]\n", "[ s5| -65/1554 0 0 0 -5/1554 -25/222 0 -55/42 1| -5/42]\n", "[---------+-----------------------------------------------------------------------------------------+---------]\n", "[ Z|-4419/154 0 0 0 -31/14 -9/2 0 -423/14 0| 2897/14]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "v=matrix(QQ,1,nv,[-65/1554,0,0,0,-5/1554,-25/222,0,-55/42] ); R=-5/42;añadeRes(v,R) #cogemos la ecuacion de x3" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[686.03 NO NO NO 688.20 39.960 NO 23.073 NO]" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "cocientesD(5)" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrr|r}\n", "{Basic} & {x}_{1} & 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"[--------+-----------------------------------------------------------------------------------------+--------]\n", "[ Z|-1026/37 0 0 0 -871/407 -774/407 0 0 -1269/55 0| 2246/11]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "corte(1) # 3" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[78.923 NO NO NO 18.146 14.885 NO NO 66.789 NO]" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "cocientesD(6)" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\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} & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 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& {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} & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 6 \\\\\n", "{x}_{3} & \\frac{3}{2} & 0 & 1 & 0 & -\\frac{1}{13} & 0 & 0 & 0 & \\frac{111}{130} & \\frac{11}{26} & \\frac{76}{13} \\\\\n", "{x}_{2} & \\frac{3}{4} & 1 & 0 & 0 & \\frac{1}{13} & 0 & 0 & 0 & \\frac{259}{260} & -\\frac{35}{52} & \\frac{41}{13} \\\\\n", "{\\color{green}{s}}_{3} & 0 & 0 & 0 & 0 & -\\frac{2}{13} & 0 & 1 & 0 & -\\frac{74}{13} & \\frac{50}{13} & \\frac{22}{13} \\\\\n", "{\\color{green}{s}}_{4} & -\\frac{9}{44} & 0 & 0 & 0 & -\\frac{1}{13} & 0 & 0 & 1 & -\\frac{259}{260} & \\frac{35}{52} & -\\frac{2}{13} \\\\\n", "{\\color{green}{s}}_{2} & \\frac{11}{4} & 0 & 0 & 0 & \\frac{12}{13} & 1 & 0 & 0 & \\frac{703}{260} & -\\frac{407}{52} & \\frac{37}{13} \\\\\n", "\\hline\n", " {Z_{ind}} & -\\frac{45}{2} & 0 & 0 & 0 & -\\frac{5}{13} & 0 & 0 & 0 & -\\frac{2331}{130} & -\\frac{387}{26} & \\frac{2584}{13}\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6| rhs]\n", "[---------+---------------------------------------------------------------------------------------------------+---------]\n", "[ x4| 1 0 0 1 0 0 0 0 0 1| 6]\n", "[ x3| 3/2 0 1 0 -1/13 0 0 0 111/130 11/26| 76/13]\n", "[ x2| 3/4 1 0 0 1/13 0 0 0 259/260 -35/52| 41/13]\n", "[ s3| 0 0 0 0 -2/13 0 1 0 -74/13 50/13| 22/13]\n", "[ s4| -9/44 0 0 0 -1/13 0 0 1 -259/260 35/52| -2/13]\n", "[ s2| 11/4 0 0 0 12/13 1 0 0 703/260 -407/52| 37/13]\n", "[---------+---------------------------------------------------------------------------------------------------+---------]\n", "[ Z| -45/2 0 0 0 -5/13 0 0 0 -2331/130 -387/26| 2584/13]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "cambio(6,6)" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[110.00 NO NO NO 5.0000 NO NO NO 18.000 NO]" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "cocientesD(5)" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {b} \\\\\n", "\\hline\n", " {x}_{4} & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 6 \\\\\n", "{x}_{3} & \\frac{75}{44} & 0 & 1 & 0 & 0 & 0 & 0 & -1 & \\frac{37}{20} & -\\frac{1}{4} & 6 \\\\\n", "{x}_{2} & \\frac{6}{11} & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 3 \\\\\n", "{\\color{green}{s}}_{3} & \\frac{9}{22} & 0 & 0 & 0 & 0 & 0 & 1 & -2 & -\\frac{37}{10} & \\frac{5}{2} & 2 \\\\\n", "{\\color{green}{s}}_{1} & \\frac{117}{44} & 0 & 0 & 0 & 1 & 0 & 0 & -13 & \\frac{259}{20} & -\\frac{35}{4} & 2 \\\\\n", "{\\color{green}{s}}_{2} & \\frac{13}{44} & 0 & 0 & 0 & 0 & 1 & 0 & 12 & -\\frac{37}{4} & \\frac{1}{4} & 1 \\\\\n", "\\hline\n", " {Z_{ind}} & -\\frac{945}{44} & 0 & 0 & 0 & 0 & 0 & 0 & -5 & -\\frac{259}{20} & -\\frac{73}{4} & 198\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {b} \\\\\n", "\\hline\n", " {x}_{4} & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 6 \\\\\n", "{x}_{3} & \\frac{75}{44} & 0 & 1 & 0 & 0 & 0 & 0 & -1 & \\frac{37}{20} & -\\frac{1}{4} & 6 \\\\\n", "{x}_{2} & \\frac{6}{11} & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 3 \\\\\n", "{\\color{green}{s}}_{3} & \\frac{9}{22} & 0 & 0 & 0 & 0 & 0 & 1 & -2 & -\\frac{37}{10} & \\frac{5}{2} & 2 \\\\\n", "{\\color{green}{s}}_{1} & \\frac{117}{44} & 0 & 0 & 0 & 1 & 0 & 0 & -13 & \\frac{259}{20} & -\\frac{35}{4} & 2 \\\\\n", "{\\color{green}{s}}_{2} & \\frac{13}{44} & 0 & 0 & 0 & 0 & 1 & 0 & 12 & -\\frac{37}{4} & \\frac{1}{4} & 1 \\\\\n", "\\hline\n", " {Z_{ind}} & -\\frac{945}{44} & 0 & 0 & 0 & 0 & 0 & 0 & -5 & -\\frac{259}{20} & -\\frac{73}{4} & 198\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6| rhs]\n", "[-------+-------------------------------------------------------------------------------+-------]\n", "[ x4| 1 0 0 1 0 0 0 0 0 1| 6]\n", "[ x3| 75/44 0 1 0 0 0 0 -1 37/20 -1/4| 6]\n", "[ x2| 6/11 1 0 0 0 0 0 1 0 0| 3]\n", "[ s3| 9/22 0 0 0 0 0 1 -2 -37/10 5/2| 2]\n", "[ s1| 117/44 0 0 0 1 0 0 -13 259/20 -35/4| 2]\n", "[ s2| 13/44 0 0 0 0 1 0 12 -37/4 1/4| 1]\n", "[-------+-------------------------------------------------------------------------------+-------]\n", "[ Z|-945/44 0 0 0 0 0 0 -5 -259/20 -73/4| 198]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "cambio(5,5)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "SageMath 9.5", "language": "sage", "name": "sagemath" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.11.2" } }, "nbformat": 4, "nbformat_minor": 4 }