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{\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & \\frac{1}{4} & 2 & \\frac{1}{2} & \\frac{9}{4} & 0 & \\frac{1}{2} & 1 & 0 & 0 & -\\frac{1}{4} & 11 \\\\\n", "{\\color{green}{s}}_{2} & -\\frac{1}{2} & 1 & -1 & \\frac{11}{2} & 0 & 0 & 0 & 1 & 0 & -\\frac{1}{2} & 8 \\\\\n", "{\\color{green}{s}}_{3} & \\frac{1}{4} & 3 & \\frac{1}{2} & \\frac{1}{4} & 0 & -\\frac{1}{2} & 0 & 0 & 1 & -\\frac{1}{4} & 25 \\\\\n", "{x}_{5} & \\frac{3}{4} & -1 & \\frac{1}{2} & -\\frac{5}{4} & 1 & \\frac{1}{2} & 0 & 0 & 0 & \\frac{1}{4} & 5 \\\\\n", "\\hline\n", " {Z_{ind}} & -5 & 34 & 2 & 43 & 0 & 6 & 0 & 0 & 0 & -5 & 100\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {x}_{5} & {x}_{6} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & \\frac{1}{4} & 2 & \\frac{1}{2} & \\frac{9}{4} & 0 & \\frac{1}{2} & 1 & 0 & 0 & -\\frac{1}{4} & 11 \\\\\n", "{\\color{green}{s}}_{2} & -\\frac{1}{2} & 1 & -1 & \\frac{11}{2} & 0 & 0 & 0 & 1 & 0 & -\\frac{1}{2} & 8 \\\\\n", "{\\color{green}{s}}_{3} & \\frac{1}{4} & 3 & \\frac{1}{2} & \\frac{1}{4} & 0 & -\\frac{1}{2} & 0 & 0 & 1 & -\\frac{1}{4} & 25 \\\\\n", "{x}_{5} & \\frac{3}{4} & -1 & \\frac{1}{2} & -\\frac{5}{4} & 1 & \\frac{1}{2} & 0 & 0 & 0 & \\frac{1}{4} & 5 \\\\\n", "\\hline\n", " {Z_{ind}} & -5 & 34 & 2 & 43 & 0 & 6 & 0 & 0 & 0 & -5 & 100\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 x5 x6 s1 s2 s3 s4| rhs]\n", "[----+-------------------------------------------------+----]\n", "[ s1| 1/4 2 1/2 9/4 0 1/2 1 0 0 -1/4| 11]\n", "[ s2|-1/2 1 -1 11/2 0 0 0 1 0 -1/2| 8]\n", "[ s3| 1/4 3 1/2 1/4 0 -1/2 0 0 1 -1/4| 25]\n", "[ x5| 3/4 -1 1/2 -5/4 1 1/2 0 0 0 1/4| 5]\n", "[----+-------------------------------------------------+----]\n", "[ Z| -5 34 2 43 0 6 0 0 0 -5| 100]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "cambio( 2 , 4 )\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {x}_{5} & {x}_{6} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & \\frac{5}{11} & \\frac{35}{22} & \\frac{10}{11} & 0 & 0 & \\frac{1}{2} & 1 & -\\frac{9}{22} & 0 & -\\frac{1}{22} & \\frac{85}{11} \\\\\n", "{x}_{4} & -\\frac{1}{11} & \\frac{2}{11} & -\\frac{2}{11} & 1 & 0 & 0 & 0 & \\frac{2}{11} & 0 & -\\frac{1}{11} & \\frac{16}{11} \\\\\n", "{\\color{green}{s}}_{3} & \\frac{3}{11} & \\frac{65}{22} & \\frac{6}{11} & 0 & 0 & -\\frac{1}{2} & 0 & -\\frac{1}{22} & 1 & -\\frac{5}{22} & \\frac{271}{11} \\\\\n", "{x}_{5} & \\frac{7}{11} & -\\frac{17}{22} & \\frac{3}{11} & 0 & 1 & \\frac{1}{2} & 0 & \\frac{5}{22} & 0 & \\frac{3}{22} & \\frac{75}{11} \\\\\n", "\\hline\n", " {Z_{ind}} & -\\frac{12}{11} & \\frac{288}{11} & \\frac{108}{11} & 0 & 0 & 6 & 0 & -\\frac{86}{11} & 0 & -\\frac{12}{11} & \\frac{1788}{11}\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {x}_{5} & {x}_{6} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & \\frac{5}{11} & \\frac{35}{22} & \\frac{10}{11} & 0 & 0 & \\frac{1}{2} & 1 & -\\frac{9}{22} & 0 & -\\frac{1}{22} & \\frac{85}{11} \\\\\n", "{x}_{4} & -\\frac{1}{11} & \\frac{2}{11} & -\\frac{2}{11} & 1 & 0 & 0 & 0 & \\frac{2}{11} & 0 & -\\frac{1}{11} & \\frac{16}{11} \\\\\n", "{\\color{green}{s}}_{3} & \\frac{3}{11} & \\frac{65}{22} & \\frac{6}{11} & 0 & 0 & -\\frac{1}{2} & 0 & -\\frac{1}{22} & 1 & -\\frac{5}{22} & \\frac{271}{11} \\\\\n", "{x}_{5} & \\frac{7}{11} & -\\frac{17}{22} & \\frac{3}{11} & 0 & 1 & \\frac{1}{2} & 0 & \\frac{5}{22} & 0 & \\frac{3}{22} & \\frac{75}{11} \\\\\n", "\\hline\n", " {Z_{ind}} & -\\frac{12}{11} & \\frac{288}{11} & \\frac{108}{11} & 0 & 0 & 6 & 0 & -\\frac{86}{11} & 0 & -\\frac{12}{11} & \\frac{1788}{11}\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 x5 x6 s1 s2 s3 s4| rhs]\n", "[-------+-------------------------------------------------------------------------------+-------]\n", "[ s1| 5/11 35/22 10/11 0 0 1/2 1 -9/22 0 -1/22| 85/11]\n", "[ x4| -1/11 2/11 -2/11 1 0 0 0 2/11 0 -1/11| 16/11]\n", "[ s3| 3/11 65/22 6/11 0 0 -1/2 0 -1/22 1 -5/22| 271/11]\n", "[ x5| 7/11 -17/22 3/11 0 1 1/2 0 5/22 0 3/22| 75/11]\n", "[-------+-------------------------------------------------------------------------------+-------]\n", "[ Z| -12/11 288/11 108/11 0 0 6 0 -86/11 0 -12/11|1788/11]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "cambio( 1 , 2 )\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {x}_{5} & {x}_{6} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {b} \\\\\n", "\\hline\n", " {x}_{2} & \\frac{2}{7} & 1 & \\frac{4}{7} & 0 & 0 & \\frac{11}{35} & \\frac{22}{35} & -\\frac{9}{35} & 0 & -\\frac{1}{35} & \\frac{34}{7} \\\\\n", "{x}_{4} & -\\frac{1}{7} & 0 & -\\frac{2}{7} & 1 & 0 & -\\frac{2}{35} & -\\frac{4}{35} & \\frac{8}{35} & 0 & -\\frac{3}{35} & \\frac{4}{7} \\\\\n", "{\\color{green}{s}}_{3} & -\\frac{4}{7} & 0 & -\\frac{8}{7} & 0 & 0 & -\\frac{10}{7} & -\\frac{13}{7} & \\frac{5}{7} & 1 & -\\frac{1}{7} & \\frac{72}{7} \\\\\n", "{x}_{5} & \\frac{6}{7} & 0 & \\frac{5}{7} & 0 & 1 & \\frac{26}{35} & \\frac{17}{35} & \\frac{1}{35} & 0 & \\frac{4}{35} & \\frac{74}{7} \\\\\n", "\\hline\n", " {Z_{ind}} & -\\frac{60}{7} & 0 & -\\frac{36}{7} & 0 & 0 & -\\frac{78}{35} & -\\frac{576}{35} & -\\frac{38}{35} & 0 & -\\frac{12}{35} & \\frac{2028}{7}\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {x}_{5} & {x}_{6} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {b} \\\\\n", "\\hline\n", " {x}_{2} & \\frac{2}{7} & 1 & \\frac{4}{7} & 0 & 0 & \\frac{11}{35} & \\frac{22}{35} & -\\frac{9}{35} & 0 & -\\frac{1}{35} & \\frac{34}{7} \\\\\n", "{x}_{4} & -\\frac{1}{7} & 0 & -\\frac{2}{7} & 1 & 0 & -\\frac{2}{35} & -\\frac{4}{35} & \\frac{8}{35} & 0 & -\\frac{3}{35} & \\frac{4}{7} \\\\\n", "{\\color{green}{s}}_{3} & -\\frac{4}{7} & 0 & -\\frac{8}{7} & 0 & 0 & -\\frac{10}{7} & -\\frac{13}{7} & \\frac{5}{7} & 1 & -\\frac{1}{7} & \\frac{72}{7} \\\\\n", "{x}_{5} & \\frac{6}{7} & 0 & \\frac{5}{7} & 0 & 1 & \\frac{26}{35} & \\frac{17}{35} & \\frac{1}{35} & 0 & \\frac{4}{35} & \\frac{74}{7} \\\\\n", "\\hline\n", " {Z_{ind}} & -\\frac{60}{7} & 0 & -\\frac{36}{7} & 0 & 0 & -\\frac{78}{35} & -\\frac{576}{35} & -\\frac{38}{35} & 0 & -\\frac{12}{35} & \\frac{2028}{7}\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 x5 x6 s1 s2 s3 s4| rhs]\n", "[-------+-------------------------------------------------------------------------------+-------]\n", "[ x2| 2/7 1 4/7 0 0 11/35 22/35 -9/35 0 -1/35| 34/7]\n", "[ x4| -1/7 0 -2/7 1 0 -2/35 -4/35 8/35 0 -3/35| 4/7]\n", "[ s3| -4/7 0 -8/7 0 0 -10/7 -13/7 5/7 1 -1/7| 72/7]\n", "[ x5| 6/7 0 5/7 0 1 26/35 17/35 1/35 0 4/35| 74/7]\n", "[-------+-------------------------------------------------------------------------------+-------]\n", "[ Z| -60/7 0 -36/7 0 0 -78/35 -576/35 -38/35 0 -12/35| 2028/7]" ] }, "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=6 # número de variables x's\n", "m=4 # número de restricciones (distintas de las de signo)\n", "\n", "c=matrix(QQ,1,n,[10,14,12,18,20,16] ) # vector de costos\n", "\n", "A=matrix(QQ,m,n,[ # coeficientes de las variables x's\n", "[1,1,1,1,1,1],\n", "[1,-1,0,3,2,1],\n", "[1,2,1,-1,1,0],\n", "[3,-4,2,-5,4,2]\n", "])\n", "\n", "b=matrix(QQ,m,1,[16,18,30,20]) # vector de la derecha\n", "\n", "\n", "######################################################\n", "############### VARIABLES DE HOLGURA ################\n", "\n", "\n", "h=matrix(ZZ,1,m,[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", "\n", "\n", "\n", "\n", "####################################################################\n", "############ HASTA AQUÍ LOS DATOS ################################\n", "####################################################################\n", "\n", "\n", "\n", "\n", "\n", "load('https://sage.unex.es/501708/simplex2023Auto.sage')\n" ] }, { "cell_type": "code", "execution_count": 6, "id": "c8e81e51", "metadata": { "scrolled": true }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{rrrr}\n", "\\frac{22}{35} & -\\frac{9}{35} & 0 & -\\frac{1}{35} \\\\\n", "-\\frac{4}{35} & \\frac{8}{35} & 0 & -\\frac{3}{35} \\\\\n", "-\\frac{13}{7} & \\frac{5}{7} & 1 & -\\frac{1}{7} \\\\\n", "\\frac{17}{35} & \\frac{1}{35} & 0 & \\frac{4}{35}\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{rrrr}\n", "\\frac{22}{35} & -\\frac{9}{35} & 0 & -\\frac{1}{35} \\\\\n", "-\\frac{4}{35} & \\frac{8}{35} & 0 & -\\frac{3}{35} \\\\\n", "-\\frac{13}{7} & \\frac{5}{7} & 1 & -\\frac{1}{7} \\\\\n", "\\frac{17}{35} & \\frac{1}{35} & 0 & \\frac{4}{35}\n", "\\end{array}\\right)$$" ], "text/plain": [ "[22/35 -9/35 0 -1/35]\n", "[-4/35 8/35 0 -3/35]\n", "[-13/7 5/7 1 -1/7]\n", "[17/35 1/35 0 4/35]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "show(BM1)" ] }, { "cell_type": "markdown", "id": "31286f11", "metadata": {}, "source": [ "# Problema b paramétrico" ] }, { "cell_type": "code", "execution_count": 2, "id": "29763803", "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrr|rr}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {x}_{5} & {x}_{6} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {b} & {b_1} \\\\\n", "\\hline\n", " {x}_{2} & \\frac{2}{7} & 1 & \\frac{4}{7} & 0 & 0 & \\frac{11}{35} & \\frac{22}{35} & -\\frac{9}{35} & 0 & -\\frac{1}{35} & \\frac{34}{7} & -\\frac{11}{35} \\\\\n", "{x}_{4} & -\\frac{1}{7} & 0 & -\\frac{2}{7} & 1 & 0 & -\\frac{2}{35} & -\\frac{4}{35} & \\frac{8}{35} & 0 & -\\frac{3}{35} & \\frac{4}{7} & \\frac{2}{35} \\\\\n", "{\\color{green}{s}}_{3} & -\\frac{4}{7} & 0 & -\\frac{8}{7} & 0 & 0 & -\\frac{10}{7} & -\\frac{13}{7} & \\frac{5}{7} & 1 & -\\frac{1}{7} & \\frac{72}{7} & \\frac{24}{7} \\\\\n", "{x}_{5} & \\frac{6}{7} & 0 & \\frac{5}{7} & 0 & 1 & \\frac{26}{35} & \\frac{17}{35} & \\frac{1}{35} & 0 & \\frac{4}{35} & \\frac{74}{7} & \\frac{9}{35} \\\\\n", "\\hline\n", " {Z_{ind}} & -\\frac{60}{7} & 0 & -\\frac{36}{7} & 0 & 0 & -\\frac{78}{35} & -\\frac{576}{35} & -\\frac{38}{35} & 0 & -\\frac{12}{35} & \\frac{2028}{7} & \\frac{62}{35}\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrr|rr}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {x}_{5} & {x}_{6} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {b} & {b_1} \\\\\n", "\\hline\n", " {x}_{2} & \\frac{2}{7} & 1 & \\frac{4}{7} & 0 & 0 & \\frac{11}{35} & \\frac{22}{35} & -\\frac{9}{35} & 0 & -\\frac{1}{35} & \\frac{34}{7} & -\\frac{11}{35} \\\\\n", "{x}_{4} & -\\frac{1}{7} & 0 & -\\frac{2}{7} & 1 & 0 & -\\frac{2}{35} & -\\frac{4}{35} & \\frac{8}{35} & 0 & -\\frac{3}{35} & \\frac{4}{7} & \\frac{2}{35} \\\\\n", "{\\color{green}{s}}_{3} & -\\frac{4}{7} & 0 & -\\frac{8}{7} & 0 & 0 & -\\frac{10}{7} & -\\frac{13}{7} & \\frac{5}{7} & 1 & -\\frac{1}{7} & \\frac{72}{7} & \\frac{24}{7} \\\\\n", "{x}_{5} & \\frac{6}{7} & 0 & \\frac{5}{7} & 0 & 1 & \\frac{26}{35} & \\frac{17}{35} & \\frac{1}{35} & 0 & \\frac{4}{35} & \\frac{74}{7} & \\frac{9}{35} \\\\\n", "\\hline\n", " {Z_{ind}} & -\\frac{60}{7} & 0 & -\\frac{36}{7} & 0 & 0 & -\\frac{78}{35} & -\\frac{576}{35} & -\\frac{38}{35} & 0 & -\\frac{12}{35} & \\frac{2028}{7} & \\frac{62}{35}\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 x5 x6 s1 s2 s3 s4| rhs rhs1]\n", "[-------+-------------------------------------------------------------------------------+---------------]\n", "[ x2| 2/7 1 4/7 0 0 11/35 22/35 -9/35 0 -1/35| 34/7 -11/35]\n", "[ x4| -1/7 0 -2/7 1 0 -2/35 -4/35 8/35 0 -3/35| 4/7 2/35]\n", "[ s3| -4/7 0 -8/7 0 0 -10/7 -13/7 5/7 1 -1/7| 72/7 24/7]\n", "[ x5| 6/7 0 5/7 0 1 26/35 17/35 1/35 0 4/35| 74/7 9/35]\n", "[-------+-------------------------------------------------------------------------------+---------------]\n", "[ Z| -60/7 0 -36/7 0 0 -78/35 -576/35 -38/35 0 -12/35| 2028/7 62/35]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "bp=matrix(QQ,m,1,[0,1,3,2]); param1b(bp) " ] }, { "cell_type": "code", "execution_count": 4, "id": "463fd6f9", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[ NO NO NO NO NO NO NO 4.2222 NO 12.000]" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "cocientesD(1)" ] }, { "cell_type": "markdown", "id": "a3eae5a0", "metadata": {}, "source": [ "Calcula los valores del parámetro $\\lambda$, para los que todas las coordenadas de $b(\\lambda)$ son positivas" ] }, { "cell_type": "code", "execution_count": 3, "id": "59545eaa", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "170/11" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "34*35/77" ] }, { "cell_type": "code", "execution_count": 8, "id": "6443f431", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[ NO NO NO NO NO NO NO 4.2222 NO 12.000]" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "cocientesD(1)" ] }, { "cell_type": "code", "execution_count": 5, "id": "ed732fbe", "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrr|rr}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {x}_{5} & {x}_{6} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {b} & {b_1} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{2} & -\\frac{10}{9} & -\\frac{35}{9} & -\\frac{20}{9} & 0 & 0 & -\\frac{11}{9} & -\\frac{22}{9} & 1 & 0 & \\frac{1}{9} & -\\frac{170}{9} & \\frac{11}{9} \\\\\n", "{x}_{4} & \\frac{1}{9} & \\frac{8}{9} & \\frac{2}{9} & 1 & 0 & \\frac{2}{9} & \\frac{4}{9} & 0 & 0 & -\\frac{1}{9} & \\frac{44}{9} & -\\frac{2}{9} \\\\\n", "{\\color{green}{s}}_{3} & \\frac{2}{9} & \\frac{25}{9} & \\frac{4}{9} & 0 & 0 & -\\frac{5}{9} & -\\frac{1}{9} & 0 & 1 & -\\frac{2}{9} & \\frac{214}{9} & \\frac{23}{9} \\\\\n", "{x}_{5} & \\frac{8}{9} & \\frac{1}{9} & \\frac{7}{9} & 0 & 1 & \\frac{7}{9} & \\frac{5}{9} & 0 & 0 & \\frac{1}{9} & \\frac{100}{9} & \\frac{2}{9} \\\\\n", "\\hline\n", " {Z_{ind}} & -\\frac{88}{9} & -\\frac{38}{9} & -\\frac{68}{9} & 0 & 0 & -\\frac{32}{9} & -\\frac{172}{9} & 0 & 0 & -\\frac{2}{9} & \\frac{2792}{9} & \\frac{4}{9}\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrr|rr}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {x}_{5} & {x}_{6} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {b} & {b_1} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{2} & -\\frac{10}{9} & -\\frac{35}{9} & -\\frac{20}{9} & 0 & 0 & -\\frac{11}{9} & -\\frac{22}{9} & 1 & 0 & \\frac{1}{9} & -\\frac{170}{9} & \\frac{11}{9} \\\\\n", "{x}_{4} & \\frac{1}{9} & \\frac{8}{9} & \\frac{2}{9} & 1 & 0 & \\frac{2}{9} & \\frac{4}{9} & 0 & 0 & -\\frac{1}{9} & \\frac{44}{9} & -\\frac{2}{9} \\\\\n", "{\\color{green}{s}}_{3} & \\frac{2}{9} & \\frac{25}{9} & \\frac{4}{9} & 0 & 0 & -\\frac{5}{9} & -\\frac{1}{9} & 0 & 1 & -\\frac{2}{9} & \\frac{214}{9} & \\frac{23}{9} \\\\\n", "{x}_{5} & \\frac{8}{9} & \\frac{1}{9} & \\frac{7}{9} & 0 & 1 & \\frac{7}{9} & \\frac{5}{9} & 0 & 0 & \\frac{1}{9} & \\frac{100}{9} & \\frac{2}{9} \\\\\n", "\\hline\n", " {Z_{ind}} & -\\frac{88}{9} & -\\frac{38}{9} & -\\frac{68}{9} & 0 & 0 & -\\frac{32}{9} & -\\frac{172}{9} & 0 & 0 & -\\frac{2}{9} & \\frac{2792}{9} & \\frac{4}{9}\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 x5 x6 s1 s2 s3 s4| rhs rhs1]\n", "[------+---------------------------------------------------------------------+-------------]\n", "[ s2| -10/9 -35/9 -20/9 0 0 -11/9 -22/9 1 0 1/9|-170/9 11/9]\n", "[ x4| 1/9 8/9 2/9 1 0 2/9 4/9 0 0 -1/9| 44/9 -2/9]\n", "[ s3| 2/9 25/9 4/9 0 0 -5/9 -1/9 0 1 -2/9| 214/9 23/9]\n", "[ x5| 8/9 1/9 7/9 0 1 7/9 5/9 0 0 1/9| 100/9 2/9]\n", "[------+---------------------------------------------------------------------+-------------]\n", "[ Z| -88/9 -38/9 -68/9 0 0 -32/9 -172/9 0 0 -2/9|2792/9 4/9]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "cambio(1,8)" ] }, { "cell_type": "code", "execution_count": 6, "id": "c29b89c4", "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrr|rr}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {x}_{5} & {x}_{6} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {b} & {b_1} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{2} & -1 & -3 & -2 & 1 & 0 & -1 & -2 & 1 & 0 & 0 & -14 & 1 \\\\\n", "{\\color{green}{s}}_{4} & -1 & -8 & -2 & -9 & 0 & -2 & -4 & 0 & 0 & 1 & -44 & 2 \\\\\n", "{\\color{green}{s}}_{3} & 0 & 1 & 0 & -2 & 0 & -1 & -1 & 0 & 1 & 0 & 14 & 3 \\\\\n", "{x}_{5} & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 0 & 0 & 16 & 0 \\\\\n", "\\hline\n", " {Z_{ind}} & -10 & -6 & -8 & -2 & 0 & -4 & -20 & 0 & 0 & 0 & 320 & 0\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrr|rr}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {x}_{5} & {x}_{6} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {b} & {b_1} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{2} & -1 & -3 & -2 & 1 & 0 & -1 & -2 & 1 & 0 & 0 & -14 & 1 \\\\\n", "{\\color{green}{s}}_{4} & -1 & -8 & -2 & -9 & 0 & -2 & -4 & 0 & 0 & 1 & -44 & 2 \\\\\n", "{\\color{green}{s}}_{3} & 0 & 1 & 0 & -2 & 0 & -1 & -1 & 0 & 1 & 0 & 14 & 3 \\\\\n", "{x}_{5} & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 0 & 0 & 16 & 0 \\\\\n", "\\hline\n", " {Z_{ind}} & -10 & -6 & -8 & -2 & 0 & -4 & -20 & 0 & 0 & 0 & 320 & 0\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 x5 x6 s1 s2 s3 s4| rhs rhs1]\n", "[----+-------------------------------------------------+---------]\n", "[ s2| -1 -3 -2 1 0 -1 -2 1 0 0| -14 1]\n", "[ s4| -1 -8 -2 -9 0 -2 -4 0 0 1| -44 2]\n", "[ s3| 0 1 0 -2 0 -1 -1 0 1 0| 14 3]\n", "[ x5| 1 1 1 1 1 1 1 0 0 0| 16 0]\n", "[----+-------------------------------------------------+---------]\n", "[ Z| -10 -6 -8 -2 0 -4 -20 0 0 0| 320 0]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "cambio(2,10)" ] } ], "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": 5 }