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"text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {b} \\\\\n", "\\hline\n", " {x}_{1} & 1 & \\frac{40}{81} & 0 & \\frac{10}{27} & 0 & -\\frac{1}{81} & \\frac{160}{81} \\\\\n", "{\\color{green}{s}}_{2} & 0 & -\\frac{85}{27} & 0 & -\\frac{10}{9} & 1 & -\\frac{35}{27} & \\frac{1010}{27} \\\\\n", "{x}_{3} & 0 & \\frac{14}{27} & 1 & -\\frac{1}{9} & 0 & \\frac{1}{27} & \\frac{164}{27} \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & -\\frac{700}{27} & 0 & -\\frac{130}{9} & 0 & -\\frac{50}{27} & \\frac{14680}{27}\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {b} \\\\\n", "\\hline\n", " {x}_{1} & 1 & \\frac{40}{81} & 0 & \\frac{10}{27} & 0 & -\\frac{1}{81} & \\frac{160}{81} \\\\\n", "{\\color{green}{s}}_{2} & 0 & -\\frac{85}{27} & 0 & -\\frac{10}{9} & 1 & -\\frac{35}{27} & \\frac{1010}{27} \\\\\n", "{x}_{3} & 0 & \\frac{14}{27} & 1 & -\\frac{1}{9} & 0 & \\frac{1}{27} & \\frac{164}{27} \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & -\\frac{700}{27} & 0 & -\\frac{130}{9} & 0 & -\\frac{50}{27} & \\frac{14680}{27}\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 s1 s2 s3| rhs]\n", "[--------+-----------------------------------------------------+--------]\n", "[ x1| 1 40/81 0 10/27 0 -1/81| 160/81]\n", "[ s2| 0 -85/27 0 -10/9 1 -35/27| 1010/27]\n", "[ x3| 0 14/27 1 -1/9 0 1/27| 164/27]\n", "[--------+-----------------------------------------------------+--------]\n", "[ Z| 0 -700/27 0 -130/9 0 -50/27|14680/27]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "El problema es óptimo\n" ] } ], "source": [ "tipo='max' #max o min\n", "n=3 # número de variables x's\n", "m=3 # número de restricciones (distintas de las de signo)\n", "\n", "\n", "c=matrix(QQ,1,n,[60,40,70] ) # vector de costos\n", "\n", "A=matrix(QQ,m,n,[ # coeficientes de las variables x's\n", "[3,2,1],\n", "[15,25,40],\n", "[9,20,30]\n", "])\n", "\n", "b=matrix(QQ,m,1,[12,310,200]) # 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": 18, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {b} \\\\\n", "\\hline\n", " {x}_{1} & 1 & \\frac{40}{81} & 0 & \\frac{10}{27} & 0 & -\\frac{1}{81} & 0 & \\frac{160}{81} \\\\\n", "{\\color{green}{s}}_{2} & 0 & -\\frac{85}{27} & 0 & -\\frac{10}{9} & 1 & -\\frac{35}{27} & 0 & \\frac{1010}{27} \\\\\n", "{x}_{3} & 0 & \\frac{14}{27} & 1 & -\\frac{1}{9} & 0 & \\frac{1}{27} & 0 & \\frac{164}{27} \\\\\n", "{\\color{green}{s}}_{4} & 0 & \\frac{14}{27} & 0 & -\\frac{1}{9} & 0 & \\frac{1}{27} & 1 & -\\frac{25}{27} \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & -\\frac{700}{27} & 0 & -\\frac{130}{9} & 0 & -\\frac{50}{27} & 0 & \\frac{14680}{27}\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {b} \\\\\n", "\\hline\n", " {x}_{1} & 1 & \\frac{40}{81} & 0 & \\frac{10}{27} & 0 & -\\frac{1}{81} & 0 & \\frac{160}{81} \\\\\n", "{\\color{green}{s}}_{2} & 0 & -\\frac{85}{27} & 0 & -\\frac{10}{9} & 1 & -\\frac{35}{27} & 0 & \\frac{1010}{27} \\\\\n", "{x}_{3} & 0 & \\frac{14}{27} & 1 & -\\frac{1}{9} & 0 & \\frac{1}{27} & 0 & \\frac{164}{27} \\\\\n", "{\\color{green}{s}}_{4} & 0 & \\frac{14}{27} & 0 & -\\frac{1}{9} & 0 & \\frac{1}{27} & 1 & -\\frac{25}{27} \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & -\\frac{700}{27} & 0 & -\\frac{130}{9} & 0 & -\\frac{50}{27} & 0 & \\frac{14680}{27}\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 s1 s2 s3 s4| rhs]\n", "[--------+--------------------------------------------------------------+--------]\n", "[ x1| 1 40/81 0 10/27 0 -1/81 0| 160/81]\n", "[ s2| 0 -85/27 0 -10/9 1 -35/27 0| 1010/27]\n", "[ x3| 0 14/27 1 -1/9 0 1/27 0| 164/27]\n", "[ s4| 0 14/27 0 -1/9 0 1/27 1| -25/27]\n", "[--------+--------------------------------------------------------------+--------]\n", "[ Z| 0 -700/27 0 -130/9 0 -50/27 0|14680/27]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "v=matrix(QQ,1,nv,[0,0,-1,0,0,0] ); R=-7;añadeRes(v,R)" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[ NO NO NO 130.00 NO NO NO]" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "cocientesD(4)" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "scrolled": true }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {b} \\\\\n", "\\hline\n", " {x}_{1} & 1 & \\frac{20}{9} & 0 & 0 & 0 & \\frac{1}{9} & \\frac{10}{3} & -\\frac{10}{9} \\\\\n", "{\\color{green}{s}}_{2} & 0 & -\\frac{25}{3} & 0 & 0 & 1 & -\\frac{5}{3} & -10 & \\frac{140}{3} \\\\\n", "{x}_{3} & 0 & 0 & 1 & 0 & 0 & 0 & -1 & 7 \\\\\n", "{\\color{green}{s}}_{1} & 0 & -\\frac{14}{3} & 0 & 1 & 0 & -\\frac{1}{3} & -9 & \\frac{25}{3} \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & -\\frac{280}{3} & 0 & 0 & 0 & -\\frac{20}{3} & -130 & \\frac{1270}{3}\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {b} \\\\\n", "\\hline\n", " {x}_{1} & 1 & \\frac{20}{9} & 0 & 0 & 0 & \\frac{1}{9} & \\frac{10}{3} & -\\frac{10}{9} \\\\\n", "{\\color{green}{s}}_{2} & 0 & -\\frac{25}{3} & 0 & 0 & 1 & -\\frac{5}{3} & -10 & \\frac{140}{3} \\\\\n", "{x}_{3} & 0 & 0 & 1 & 0 & 0 & 0 & -1 & 7 \\\\\n", "{\\color{green}{s}}_{1} & 0 & -\\frac{14}{3} & 0 & 1 & 0 & -\\frac{1}{3} & -9 & \\frac{25}{3} \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & -\\frac{280}{3} & 0 & 0 & 0 & -\\frac{20}{3} & -130 & \\frac{1270}{3}\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 s1 s2 s3 s4| rhs]\n", "[------+------------------------------------------------+------]\n", "[ x1| 1 20/9 0 0 0 1/9 10/3| -10/9]\n", "[ s2| 0 -25/3 0 0 1 -5/3 -10| 140/3]\n", "[ x3| 0 0 1 0 0 0 -1| 7]\n", "[ s1| 0 -14/3 0 1 0 -1/3 -9| 25/3]\n", "[------+------------------------------------------------+------]\n", "[ Z| 0 -280/3 0 0 0 -20/3 -130|1270/3]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "cambio(4,4)" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {b} \\\\\n", "\\hline\n", " {x}_{1} & 1 & \\frac{20}{9} & 0 & 0 & 0 & \\frac{1}{9} & \\frac{10}{3} & 0 & -\\frac{10}{9} \\\\\n", "{\\color{green}{s}}_{2} & 0 & -\\frac{25}{3} & 0 & 0 & 1 & -\\frac{5}{3} & -10 & 0 & \\frac{140}{3} \\\\\n", "{x}_{3} & 0 & 0 & 1 & 0 & 0 & 0 & -1 & 0 & 7 \\\\\n", "{\\color{green}{s}}_{1} & 0 & -\\frac{14}{3} & 0 & 1 & 0 & -\\frac{1}{3} & -9 & 0 & \\frac{25}{3} \\\\\n", "{\\color{green}{s}}_{5} & 0 & -\\frac{20}{9} & 0 & 0 & 0 & -\\frac{1}{9} & -\\frac{10}{3} & 1 & \\frac{19}{9} \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & -\\frac{280}{3} & 0 & 0 & 0 & -\\frac{20}{3} & -130 & 0 & \\frac{1270}{3}\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {b} \\\\\n", "\\hline\n", " {x}_{1} & 1 & \\frac{20}{9} & 0 & 0 & 0 & \\frac{1}{9} & \\frac{10}{3} & 0 & -\\frac{10}{9} \\\\\n", "{\\color{green}{s}}_{2} & 0 & -\\frac{25}{3} & 0 & 0 & 1 & -\\frac{5}{3} & -10 & 0 & \\frac{140}{3} \\\\\n", "{x}_{3} & 0 & 0 & 1 & 0 & 0 & 0 & -1 & 0 & 7 \\\\\n", "{\\color{green}{s}}_{1} & 0 & -\\frac{14}{3} & 0 & 1 & 0 & -\\frac{1}{3} & -9 & 0 & \\frac{25}{3} \\\\\n", "{\\color{green}{s}}_{5} & 0 & -\\frac{20}{9} & 0 & 0 & 0 & -\\frac{1}{9} & -\\frac{10}{3} & 1 & \\frac{19}{9} \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & -\\frac{280}{3} & 0 & 0 & 0 & -\\frac{20}{3} & -130 & 0 & \\frac{1270}{3}\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 s1 s2 s3 s4 s5| rhs]\n", "[------+-------------------------------------------------------+------]\n", "[ x1| 1 20/9 0 0 0 1/9 10/3 0| -10/9]\n", "[ s2| 0 -25/3 0 0 1 -5/3 -10 0| 140/3]\n", "[ x3| 0 0 1 0 0 0 -1 0| 7]\n", "[ s1| 0 -14/3 0 1 0 -1/3 -9 0| 25/3]\n", "[ s5| 0 -20/9 0 0 0 -1/9 -10/3 1| 19/9]\n", "[------+-------------------------------------------------------+------]\n", "[ Z| 0 -280/3 0 0 0 -20/3 -130 0|1270/3]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "v=matrix(QQ,1,nv,[1,0,0,0,0,0,0] ); R=1;añadeRes(v,R)" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[ NO 42.000 NO NO NO 60.000 39.000 NO]" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "cocientesD(5)" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {b} \\\\\n", "\\hline\n", " {x}_{1} & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 \\\\\n", "{\\color{green}{s}}_{2} & 0 & -\\frac{5}{3} & 0 & 0 & 1 & -\\frac{4}{3} & 0 & -3 & \\frac{121}{3} \\\\\n", "{x}_{3} & 0 & \\frac{2}{3} & 1 & 0 & 0 & \\frac{1}{30} & 0 & -\\frac{3}{10} & \\frac{191}{30} \\\\\n", "{\\color{green}{s}}_{1} & 0 & \\frac{4}{3} & 0 & 1 & 0 & -\\frac{1}{30} & 0 & -\\frac{27}{10} & \\frac{79}{30} \\\\\n", "{\\color{green}{s}}_{4} & 0 & \\frac{2}{3} & 0 & 0 & 0 & \\frac{1}{30} & 1 & -\\frac{3}{10} & -\\frac{19}{30} \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & -\\frac{20}{3} & 0 & 0 & 0 & -\\frac{7}{3} & 0 & -39 & \\frac{1517}{3}\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {b} \\\\\n", "\\hline\n", " {x}_{1} & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 \\\\\n", "{\\color{green}{s}}_{2} & 0 & -\\frac{5}{3} & 0 & 0 & 1 & -\\frac{4}{3} & 0 & -3 & \\frac{121}{3} \\\\\n", "{x}_{3} & 0 & \\frac{2}{3} & 1 & 0 & 0 & \\frac{1}{30} & 0 & -\\frac{3}{10} & \\frac{191}{30} \\\\\n", "{\\color{green}{s}}_{1} & 0 & \\frac{4}{3} & 0 & 1 & 0 & -\\frac{1}{30} & 0 & -\\frac{27}{10} & \\frac{79}{30} \\\\\n", "{\\color{green}{s}}_{4} & 0 & \\frac{2}{3} & 0 & 0 & 0 & \\frac{1}{30} & 1 & -\\frac{3}{10} & -\\frac{19}{30} \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & -\\frac{20}{3} & 0 & 0 & 0 & -\\frac{7}{3} & 0 & -39 & \\frac{1517}{3}\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 s1 s2 s3 s4 s5| rhs]\n", "[------+-------------------------------------------------------+------]\n", "[ x1| 1 0 0 0 0 0 0 1| 1]\n", "[ s2| 0 -5/3 0 0 1 -4/3 0 -3| 121/3]\n", "[ x3| 0 2/3 1 0 0 1/30 0 -3/10|191/30]\n", "[ s1| 0 4/3 0 1 0 -1/30 0 -27/10| 79/30]\n", "[ s4| 0 2/3 0 0 0 1/30 1 -3/10|-19/30]\n", "[------+-------------------------------------------------------+------]\n", "[ Z| 0 -20/3 0 0 0 -7/3 0 -39|1517/3]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "cambio(5,7)" ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "scrolled": true }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {b} \\\\\n", "\\hline\n", " {x}_{1} & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 \\\\\n", "{\\color{green}{s}}_{2} & 0 & -\\frac{5}{3} & 0 & 0 & 1 & -\\frac{4}{3} & 0 & -3 & 0 & \\frac{121}{3} \\\\\n", "{x}_{3} & 0 & \\frac{2}{3} & 1 & 0 & 0 & \\frac{1}{30} & 0 & -\\frac{3}{10} & 0 & \\frac{191}{30} \\\\\n", "{\\color{green}{s}}_{1} & 0 & \\frac{4}{3} & 0 & 1 & 0 & -\\frac{1}{30} & 0 & -\\frac{27}{10} & 0 & \\frac{79}{30} \\\\\n", "{\\color{green}{s}}_{4} & 0 & \\frac{2}{3} & 0 & 0 & 0 & \\frac{1}{30} & 1 & -\\frac{3}{10} & 0 & -\\frac{19}{30} \\\\\n", "{\\color{green}{s}}_{6} & 0 & \\frac{2}{3} & 0 & 0 & 0 & \\frac{1}{30} & 0 & -\\frac{3}{10} & 1 & \\frac{401}{30} \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & -\\frac{20}{3} & 0 & 0 & 0 & -\\frac{7}{3} & 0 & -39 & 0 & \\frac{1517}{3}\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {b} \\\\\n", "\\hline\n", " {x}_{1} & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 \\\\\n", "{\\color{green}{s}}_{2} & 0 & -\\frac{5}{3} & 0 & 0 & 1 & -\\frac{4}{3} & 0 & -3 & 0 & \\frac{121}{3} \\\\\n", "{x}_{3} & 0 & \\frac{2}{3} & 1 & 0 & 0 & \\frac{1}{30} & 0 & -\\frac{3}{10} & 0 & \\frac{191}{30} \\\\\n", "{\\color{green}{s}}_{1} & 0 & \\frac{4}{3} & 0 & 1 & 0 & -\\frac{1}{30} & 0 & -\\frac{27}{10} & 0 & \\frac{79}{30} \\\\\n", "{\\color{green}{s}}_{4} & 0 & \\frac{2}{3} & 0 & 0 & 0 & \\frac{1}{30} & 1 & -\\frac{3}{10} & 0 & -\\frac{19}{30} \\\\\n", "{\\color{green}{s}}_{6} & 0 & \\frac{2}{3} & 0 & 0 & 0 & \\frac{1}{30} & 0 & -\\frac{3}{10} & 1 & \\frac{401}{30} \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & -\\frac{20}{3} & 0 & 0 & 0 & -\\frac{7}{3} & 0 & -39 & 0 & \\frac{1517}{3}\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 s1 s2 s3 s4 s5 s6| rhs]\n", "[------+--------------------------------------------------------------+------]\n", "[ x1| 1 0 0 0 0 0 0 1 0| 1]\n", "[ s2| 0 -5/3 0 0 1 -4/3 0 -3 0| 121/3]\n", "[ x3| 0 2/3 1 0 0 1/30 0 -3/10 0|191/30]\n", "[ s1| 0 4/3 0 1 0 -1/30 0 -27/10 0| 79/30]\n", "[ s4| 0 2/3 0 0 0 1/30 1 -3/10 0|-19/30]\n", "[ s6| 0 2/3 0 0 0 1/30 0 -3/10 1|401/30]\n", "[------+--------------------------------------------------------------+------]\n", "[ Z| 0 -20/3 0 0 0 -7/3 0 -39 0|1517/3]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "v=matrix(QQ,1,nv,[0,0,-1,0,0,0,0,0] ); R=7;añadeRes(v,R)" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[ NO NO NO NO NO NO NO 130.00 NO]" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ "cocientesD(6)" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {b} \\\\\n", "\\hline\n", " {x}_{1} & 1 & \\frac{20}{9} & 0 & 0 & 0 & \\frac{1}{9} & 0 & 0 & \\frac{10}{3} & \\frac{410}{9} \\\\\n", "{\\color{green}{s}}_{2} & 0 & -\\frac{25}{3} & 0 & 0 & 1 & -\\frac{5}{3} & 0 & 0 & -10 & -\\frac{280}{3} \\\\\n", "{x}_{3} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & -7 \\\\\n", "{\\color{green}{s}}_{1} & 0 & -\\frac{14}{3} & 0 & 1 & 0 & -\\frac{1}{3} & 0 & 0 & -9 & -\\frac{353}{3} \\\\\n", "{\\color{green}{s}}_{4} & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & -1 & -14 \\\\\n", "{\\color{green}{s}}_{5} & 0 & -\\frac{20}{9} & 0 & 0 & 0 & -\\frac{1}{9} & 0 & 1 & -\\frac{10}{3} & -\\frac{401}{9} \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & -\\frac{280}{3} & 0 & 0 & 0 & -\\frac{20}{3} & 0 & 0 & -130 & \\frac{6730}{3}\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {b} \\\\\n", "\\hline\n", " {x}_{1} & 1 & \\frac{20}{9} & 0 & 0 & 0 & \\frac{1}{9} & 0 & 0 & \\frac{10}{3} & \\frac{410}{9} \\\\\n", "{\\color{green}{s}}_{2} & 0 & -\\frac{25}{3} & 0 & 0 & 1 & -\\frac{5}{3} & 0 & 0 & -10 & -\\frac{280}{3} \\\\\n", "{x}_{3} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & -7 \\\\\n", "{\\color{green}{s}}_{1} & 0 & -\\frac{14}{3} & 0 & 1 & 0 & -\\frac{1}{3} & 0 & 0 & -9 & -\\frac{353}{3} \\\\\n", "{\\color{green}{s}}_{4} & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & -1 & -14 \\\\\n", "{\\color{green}{s}}_{5} & 0 & -\\frac{20}{9} & 0 & 0 & 0 & -\\frac{1}{9} & 0 & 1 & -\\frac{10}{3} & -\\frac{401}{9} \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & -\\frac{280}{3} & 0 & 0 & 0 & -\\frac{20}{3} & 0 & 0 & -130 & \\frac{6730}{3}\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 s1 s2 s3 s4 s5 s6| rhs]\n", "[------+--------------------------------------------------------------+------]\n", "[ x1| 1 20/9 0 0 0 1/9 0 0 10/3| 410/9]\n", "[ s2| 0 -25/3 0 0 1 -5/3 0 0 -10|-280/3]\n", "[ 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