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& {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{red}{t}}_{1} & {\\color{red}{t}}_{2} & {\\color{red}{t}}_{3} & {b} \\\\\n", "\\hline\n", " {x}_{2} & \\frac{73}{65} & 1 & 0 & -\\frac{4}{65} & 0 & -\\frac{2}{65} & \\frac{1}{13} & 0 & \\frac{2}{65} & -\\frac{1}{13} & \\frac{350}{13} \\\\\n", "{\\color{green}{s}}_{1} & -\\frac{193}{65} & 0 & 0 & -\\frac{196}{65} & 1 & -\\frac{164}{195} & -\\frac{22}{39} & -1 & \\frac{164}{195} & \\frac{22}{39} & \\frac{2440}{39} \\\\\n", "{x}_{3} & -\\frac{3}{13} & 0 & 1 & \\frac{8}{13} & 0 & -\\frac{1}{39} & -\\frac{4}{39} & 0 & \\frac{1}{39} & \\frac{4}{39} & \\frac{940}{39} \\\\\n", "\\hline\n", " {W_{ind}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 0\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3 t1 t2 t3| rhs]\n", "[--------+-----------------------------------------------------------------------------------------+--------]\n", "[ x2| 73/65 1 0 -4/65 0 -2/65 1/13 0 2/65 -1/13| 350/13]\n", "[ s1| -193/65 0 0 -196/65 1 -164/195 -22/39 -1 164/195 22/39| 2440/39]\n", "[ x3| -3/13 0 1 8/13 0 -1/39 -4/39 0 1/39 4/39| 940/39]\n", "[--------+-----------------------------------------------------------------------------------------+--------]\n", "[ W| 0 0 0 0 0 0 0 1 1 1| 0]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "El problema de la fase I es óptimo y Wopt=0. Por tanto, el original es factible\n", "Preparemos el cuadro inicial de la fase II\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$$" ], "text/plain": [ "ry" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}{\\ \\ \\ Fase\\ II}$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{\\ \\ \\ Fase\\ II}$$" ], "text/plain": [ "FII" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$$" ], "text/plain": [ "ry" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {b} \\\\\n", "\\hline\n", " {x}_{2} & \\frac{73}{65} & 1 & 0 & -\\frac{4}{65} & 0 & -\\frac{2}{65} & \\frac{1}{13} & \\frac{350}{13} \\\\\n", "{\\color{green}{s}}_{1} & -\\frac{193}{65} & 0 & 0 & -\\frac{196}{65} & 1 & -\\frac{164}{195} & -\\frac{22}{39} & \\frac{2440}{39} \\\\\n", "{x}_{3} & -\\frac{3}{13} & 0 & 1 & \\frac{8}{13} & 0 & -\\frac{1}{39} & -\\frac{4}{39} & \\frac{940}{39} \\\\\n", "\\hline\n", " {Z_{ind}} & -\\frac{14}{65} & 0 & 0 & \\frac{72}{65} & 0 & \\frac{43}{195} & \\frac{11}{39} & \\frac{7850}{39}\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {b} \\\\\n", "\\hline\n", " {x}_{2} & \\frac{73}{65} & 1 & 0 & -\\frac{4}{65} & 0 & -\\frac{2}{65} & \\frac{1}{13} & \\frac{350}{13} \\\\\n", "{\\color{green}{s}}_{1} & -\\frac{193}{65} & 0 & 0 & -\\frac{196}{65} & 1 & -\\frac{164}{195} & -\\frac{22}{39} & \\frac{2440}{39} \\\\\n", "{x}_{3} & -\\frac{3}{13} & 0 & 1 & \\frac{8}{13} & 0 & -\\frac{1}{39} & -\\frac{4}{39} & \\frac{940}{39} \\\\\n", "\\hline\n", " {Z_{ind}} & -\\frac{14}{65} & 0 & 0 & \\frac{72}{65} & 0 & \\frac{43}{195} & \\frac{11}{39} & \\frac{7850}{39}\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3| rhs]\n", "[--------+--------------------------------------------------------------+--------]\n", "[ x2| 73/65 1 0 -4/65 0 -2/65 1/13| 350/13]\n", "[ s1| -193/65 0 0 -196/65 1 -164/195 -22/39| 2440/39]\n", "[ x3| -3/13 0 1 8/13 0 -1/39 -4/39| 940/39]\n", "[--------+--------------------------------------------------------------+--------]\n", "[ Z| -14/65 0 0 72/65 0 43/195 11/39| 7850/39]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "cambio( 1 , 1 )\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {b} \\\\\n", "\\hline\n", " {x}_{1} & 1 & \\frac{65}{73} & 0 & -\\frac{4}{73} & 0 & -\\frac{2}{73} & \\frac{5}{73} & \\frac{1750}{73} \\\\\n", "{\\color{green}{s}}_{1} & 0 & \\frac{193}{73} & 0 & -\\frac{232}{73} & 1 & -\\frac{202}{219} & -\\frac{79}{219} & \\frac{29290}{219} \\\\\n", "{x}_{3} & 0 & \\frac{15}{73} & 1 & \\frac{44}{73} & 0 & -\\frac{7}{219} & -\\frac{19}{219} & \\frac{6490}{219} \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & \\frac{14}{73} & 0 & \\frac{80}{73} & 0 & \\frac{47}{219} & \\frac{65}{219} & \\frac{42950}{219}\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {b} \\\\\n", "\\hline\n", " {x}_{1} & 1 & \\frac{65}{73} & 0 & -\\frac{4}{73} & 0 & -\\frac{2}{73} & \\frac{5}{73} & \\frac{1750}{73} \\\\\n", "{\\color{green}{s}}_{1} & 0 & \\frac{193}{73} & 0 & -\\frac{232}{73} & 1 & -\\frac{202}{219} & -\\frac{79}{219} & \\frac{29290}{219} \\\\\n", "{x}_{3} & 0 & \\frac{15}{73} & 1 & \\frac{44}{73} & 0 & -\\frac{7}{219} & -\\frac{19}{219} & \\frac{6490}{219} \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & \\frac{14}{73} & 0 & \\frac{80}{73} & 0 & \\frac{47}{219} & \\frac{65}{219} & \\frac{42950}{219}\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3| rhs]\n", "[---------+---------------------------------------------------------------------+---------]\n", "[ x1| 1 65/73 0 -4/73 0 -2/73 5/73| 1750/73]\n", "[ s1| 0 193/73 0 -232/73 1 -202/219 -79/219|29290/219]\n", "[ x3| 0 15/73 1 44/73 0 -7/219 -19/219| 6490/219]\n", "[---------+---------------------------------------------------------------------+---------]\n", "[ Z| 0 14/73 0 80/73 0 47/219 65/219|42950/219]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "El problema es óptimo\n" ] } ], "source": [ "tipo='min' #max o min\n", "n=4 # número de variables x's\n", "m=3 # número de restricciones (distintas de las de signo)\n", "\n", "c=matrix(QQ,1,n,[2,3,5,4] ) # vector de costos\n", "\n", "A=matrix(QQ,m,n,[ # coeficientes de las variables x's\n", "[15,14,16,12],\n", "[19,20,15,8],\n", "[-7,-5,6,4]\n", "])\n", "\n", "b=matrix(QQ,m,1,[700,900,10]) # vector de la derecha\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", "######################################################\n", "######### Problemas Paramétricos ###########\n", " \n", "prmtr_b=0 # 1 si quieres usar un parámetro en b\n", " # 0 en caso contrario\n", "\n", "bp=matrix(QQ,m,1,[1,-1,2]) # vector de la derecha para problemas paramétricos.\n", "\n", "###################################################### \n", " \n", "prmtr_c=0 # 1 si quieres usar un parámetro en c\n", " # 0 en caso contrario\n", "\n", " \n", "cp=matrix(QQ,1,n,[-1,1,0,2] ) # vector de costos adicional para problemas paramétricos.\n", "\n", "######################################################\n", "\n", "\n", "##############################################################################\n", "####### Usando el paquete de programación lineal Pinteractive de Sage ########\n", "##############################################################################\n", "signos=[]\n", "for i in range(m):\n", " if h[0,i] == -1:\n", " signos.append(\">=\")\n", " elif h[0,i] == 1:\n", " signos.append(\"<=\")\n", " elif h[0,i] == 0:\n", " signos.append(\"==\")\n", " \n", "var_nam = []\n", "for i in range(n):\n", " k=i+1\n", " var_nam.append('x_%s' %k)\n", " \n", "PPL = InteractiveLPProblem(A, b, c, var_nam, \n", "constraint_type=signos, variable_type=\">=\", problem_type=\"min\") \n", "\n", "##############################################################################\n", "##############################################################################\n", "\n", "\n", "####################################################################\n", "############ HASTA AQUÍ LOS DATOS ################################\n", "####################################################################\n", "\n", "\n", "raya=var('ry', latex_name='===================================')\n", "show(ry)\n", "show(ry)\n", "show(PPL)\n", "show(PPL.optimal_value())\n", "show(PPL.optimal_solution())\n", "show(ry)\n", "show(ry)\n", "\n", "#load('https://sage.unex.es/501708/simplex2023Auto.sage')\n", "load('https://sage.unex.es/501708/simplex2023Auto_MC.sage')" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "jupyter": { "outputs_hidden": true } }, "outputs": [ { "data": { "text/plain": [ "71/73" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "1750/73 -23\n" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "jupyter": { "outputs_hidden": true } }, "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}_{1} & 1 & \\frac{65}{73} & 0 & -\\frac{4}{73} & 0 & -\\frac{2}{73} & \\frac{5}{73} & 0 & \\frac{1750}{73} \\\\\n", "{\\color{green}{s}}_{1} & 0 & \\frac{193}{73} & 0 & -\\frac{232}{73} & 1 & -\\frac{202}{219} & -\\frac{79}{219} & 0 & \\frac{29290}{219} \\\\\n", "{x}_{3} & 0 & \\frac{15}{73} & 1 & \\frac{44}{73} & 0 & -\\frac{7}{219} & -\\frac{19}{219} & 0 & \\frac{6490}{219} \\\\\n", "{\\color{green}{s}}_{4} & 0 & -65 & 0 & -69 & 0 & -71 & -5 & 1 & -71 \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & \\frac{14}{73} & 0 & \\frac{80}{73} & 0 & \\frac{47}{219} & \\frac{65}{219} & 0 & \\frac{42950}{219}\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}_{1} & 1 & \\frac{65}{73} & 0 & -\\frac{4}{73} & 0 & -\\frac{2}{73} & \\frac{5}{73} & 0 & \\frac{1750}{73} \\\\\n", "{\\color{green}{s}}_{1} & 0 & \\frac{193}{73} & 0 & -\\frac{232}{73} & 1 & -\\frac{202}{219} & -\\frac{79}{219} & 0 & \\frac{29290}{219} \\\\\n", "{x}_{3} & 0 & \\frac{15}{73} & 1 & \\frac{44}{73} & 0 & -\\frac{7}{219} & -\\frac{19}{219} & 0 & \\frac{6490}{219} \\\\\n", "{\\color{green}{s}}_{4} & 0 & -65 & 0 & -69 & 0 & -71 & -5 & 1 & -71 \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & \\frac{14}{73} & 0 & \\frac{80}{73} & 0 & \\frac{47}{219} & \\frac{65}{219} & 0 & \\frac{42950}{219}\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3 s4| rhs]\n", "[---------+-------------------------------------------------------------------------------+---------]\n", "[ x1| 1 65/73 0 -4/73 0 -2/73 5/73 0| 1750/73]\n", "[ s1| 0 193/73 0 -232/73 1 -202/219 -79/219 0|29290/219]\n", "[ x3| 0 15/73 1 44/73 0 -7/219 -19/219 0| 6490/219]\n", "[ s4| 0 -65 0 -69 0 -71 -5 1| -71]\n", "[---------+-------------------------------------------------------------------------------+---------]\n", "[ Z| 0 14/73 0 80/73 0 47/219 65/219 0|42950/219]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "v=matrix(QQ,1,nv,[0,-65,0,-69,0,-71,-5] ); R=-71;\n", "añadeRes(v,R)" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "jupyter": { "outputs_hidden": true } }, "outputs": [ { "data": { "text/plain": [ "[ NO -0.0029505 NO -0.015882 NO -0.0030227 -0.059361 NO]" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "cocientesD(4)" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "jupyter": { "outputs_hidden": true } }, "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}_{1} & 1 & 0 & 0 & -1 & 0 & -1 & 0 & \\frac{1}{73} & 23 \\\\\n", "{\\color{green}{s}}_{1} & 0 & 0 & 0 & -\\frac{389}{65} & 1 & -\\frac{743}{195} & -\\frac{22}{39} & \\frac{193}{4745} & \\frac{25517}{195} \\\\\n", "{x}_{3} & 0 & 0 & 1 & \\frac{5}{13} & 0 & -\\frac{10}{39} & -\\frac{4}{39} & \\frac{3}{949} & \\frac{1147}{39} \\\\\n", "{x}_{2} & 0 & 1 & 0 & \\frac{69}{65} & 0 & \\frac{71}{65} & \\frac{1}{13} & -\\frac{1}{65} & \\frac{71}{65} \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & 0 & \\frac{58}{65} & 0 & \\frac{1}{195} & \\frac{11}{39} & \\frac{14}{4745} & \\frac{38284}{195}\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}_{1} & 1 & 0 & 0 & -1 & 0 & -1 & 0 & \\frac{1}{73} & 23 \\\\\n", "{\\color{green}{s}}_{1} & 0 & 0 & 0 & -\\frac{389}{65} & 1 & -\\frac{743}{195} & -\\frac{22}{39} & \\frac{193}{4745} & \\frac{25517}{195} \\\\\n", "{x}_{3} & 0 & 0 & 1 & \\frac{5}{13} & 0 & -\\frac{10}{39} & -\\frac{4}{39} & \\frac{3}{949} & \\frac{1147}{39} \\\\\n", "{x}_{2} & 0 & 1 & 0 & \\frac{69}{65} & 0 & \\frac{71}{65} & \\frac{1}{13} & -\\frac{1}{65} & \\frac{71}{65} \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & 0 & \\frac{58}{65} & 0 & \\frac{1}{195} & \\frac{11}{39} & \\frac{14}{4745} & \\frac{38284}{195}\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3 s4| rhs]\n", "[---------+-------------------------------------------------------------------------------+---------]\n", "[ x1| 1 0 0 -1 0 -1 0 1/73| 23]\n", "[ s1| 0 0 0 -389/65 1 -743/195 -22/39 193/4745|25517/195]\n", "[ x3| 0 0 1 5/13 0 -10/39 -4/39 3/949| 1147/39]\n", "[ x2| 0 1 0 69/65 0 71/65 1/13 -1/65| 71/65]\n", "[---------+-------------------------------------------------------------------------------+---------]\n", "[ Z| 0 0 0 58/65 0 1/195 11/39 14/4745|38284/195]" ] }, "metadata": {}, "output_type": "display_data" } ], 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-\\frac{10}{39} & -\\frac{4}{39} & \\frac{3}{949} & 0 & \\frac{1147}{39} \\\\\n", "{x}_{2} & 0 & 1 & 0 & \\frac{69}{65} & 0 & \\frac{71}{65} & \\frac{1}{13} & -\\frac{1}{65} & 0 & \\frac{71}{65} \\\\\n", "{\\color{green}{s}}_{5} & 0 & 0 & 0 & -4 & 0 & -6 & -5 & -\\frac{6}{59} & 1 & -6 \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & 0 & \\frac{58}{65} & 0 & \\frac{1}{195} & \\frac{11}{39} & \\frac{14}{4745} & 0 & \\frac{38284}{195}\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\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 & -1 & 0 & -1 & 0 & \\frac{1}{73} & 0 & 23 \\\\\n", "{\\color{green}{s}}_{1} & 0 & 0 & 0 & -\\frac{389}{65} & 1 & -\\frac{743}{195} & -\\frac{22}{39} & \\frac{193}{4745} & 0 & \\frac{25517}{195} \\\\\n", 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{\\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 & 0 & -\\frac{1076}{411} & 0 & 0 & 0 & 0 & -\\frac{10849}{17810} & \\frac{1127}{822} & -\\frac{1105}{274} & \\frac{8693}{411} \\\\\n", "{\\color{green}{s}}_{1} & 0 & 0 & 0 & -\\frac{4636}{411} & 1 & 0 & 0 & 0 & -\\frac{111823}{53430} & \\frac{10117}{2466} & -\\frac{3065}{274} & \\frac{51361}{411} \\\\\n", "{x}_{3} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -\\frac{5}{39} & \\frac{1}{9} & 0 & 29 \\\\\n", "{x}_{2} & 0 & 1 & 0 & \\frac{1174}{411} & 0 & 0 & 0 & 0 & \\frac{11571}{17810} & -\\frac{357}{274} & \\frac{965}{274} & \\frac{1283}{411} \\\\\n", "{\\color{green}{s}}_{2} & 0 & 0 & 0 & -\\frac{84}{137} & 0 & 1 & 0 & 0 & -\\frac{8961}{17810} & \\frac{1363}{822} & -\\frac{1695}{274} & -\\frac{96}{137} \\\\\n", "{\\color{green}{s}}_{3} & 0 & 0 & 0 & \\frac{6}{137} & 0 & 0 & 1 & 0 & \\frac{2194}{8905} & -\\frac{331}{137} & \\frac{1455}{137} & \\frac{46}{137} \\\\\n", "{\\color{green}{s}}_{4} & 0 & 0 & 0 & \\frac{30149}{411} & 0 & 0 & 0 & 1 & \\frac{68912}{8905} & \\frac{8614}{411} & -\\frac{21535}{137} & \\frac{34456}{411} \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & 0 & \\frac{2}{3} & 0 & 0 & 0 & 0 & -\\frac{7}{78} & \\frac{11}{18} & -\\frac{5}{2} & \\frac{590}{3}\n", "\\end{array}\\right)$ " ], "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}_{1} & 1 & 0 & 0 & -\\frac{1076}{411} & 0 & 0 & 0 & 0 & -\\frac{10849}{17810} & \\frac{1127}{822} & -\\frac{1105}{274} & \\frac{8693}{411} \\\\\n", "{\\color{green}{s}}_{1} & 0 & 0 & 0 & -\\frac{4636}{411} & 1 & 0 & 0 & 0 & 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