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& -2 & 0 & 0 & 1 & 14 \\\\\n", "\\hline\n", " {Z_{ind}} & 17 & 12 & 7 & 20 & 0 & 0 & 0 & 0\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3|rhs]\n", "[---+---------------------------+---]\n", "[ s1| 1 6 -7 7 1 0 0| 20]\n", "[ s2| 6 -7 5 1 0 1 0| 16]\n", "[ s3| 4 4 2 -2 0 0 1| 14]\n", "[---+---------------------------+---]\n", "[ Z| 17 12 7 20 0 0 0| 0]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ " \n", " \n", "cambio( 1 , 4 )\n", "cambio( 2 , 3 )\n", "cambio( 3 , 2 )\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {b} \\\\\n", "\\hline\n", " {x}_{4} & \\frac{35}{24} & 0 & 0 & 1 & \\frac{17}{120} & \\frac{1}{6} & \\frac{19}{240} & \\frac{793}{120} \\\\\n", "{x}_{3} & \\frac{47}{24} & 0 & 1 & 0 & 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"\n", "\n", "\n", "######################################################\n", "############### VARIABLES DE HOLGURA ################\n", "\n", "\n", "h=matrix(ZZ,1,m,[1,1,1]) # variables de holgura: \n", " # Pon 1 si va sumando, \n", " # -1 si va restando y \n", " # 0 si no hay variable de holgura.\n", "\n", "#######################################################\n", "\n", "####################################################################\n", "############ HASTA AQUÍ LOS DATOS ################################\n", "####################################################################\n", "\n", "\n", "#load('https://sage.unex.es/501708/simplex2023Auto.sage')\n", "load('https://sage.unex.es/501708/simplex2023Auto_MC.sage')\n" ] }, { "cell_type": "code", "execution_count": 64, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left[1, 2, 3, 4, 5, 6, 7\\right]$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left[1, 2, 3, 4, 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0 & 0 & -\\frac{69}{16} & 0 & -\\frac{11}{8} & 1 & -\\frac{1}{2} \\\\\n", "\\hline\n", " {Z_{ind}} & -\\frac{1791}{56} & 0 & 0 & 0 & -\\frac{13}{5} & 0 & 0 & -\\frac{81}{4} & 0 & -\\frac{9}{10} & 0 & \\frac{1016}{5}\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6 s7| rhs]\n", "[--------+--------------------------------------------------------------------------------------------------+--------]\n", "[ x4| 149/112 0 0 1 1/10 0 0 -1/8 0 3/20 0| 31/5]\n", "[ x3| 13/7 0 1 0 0 0 0 1 0 0 0| 6]\n", "[ x2| 25/32 1 0 0 1/20 0 0 21/16 0 -7/40 0| 31/10]\n", "[ s3| -5/28 0 0 0 0 0 1 -15/2 0 1 0| 2]\n", "[ s2| 191/224 0 0 0 1/4 1 0 69/16 0 -11/8 0| 3/2]\n", "[ s5| 1/14 0 0 0 1/5 0 0 3 1 -6/5 0| 2/5]\n", "[ s7| -33/224 0 0 0 -1/4 0 0 -69/16 0 -11/8 1| -1/2]\n", "[--------+--------------------------------------------------------------------------------------------------+--------]\n", "[ Z|-1791/56 0 0 0 -13/5 0 0 -81/4 0 -9/10 0| 1016/5]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "corte(5)" ] }, { "cell_type": "code", "execution_count": 78, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[ 217.09 NO NO NO 10.400 NO NO 4.6957 NO 0.65455 NO]" ] }, "execution_count": 78, "metadata": {}, "output_type": "execute_result" } ], "source": [ "cocientesD(7)" ] }, { "cell_type": "code", "execution_count": 79, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\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}_{4} & \\frac{46}{35} & 0 & 0 & 1 & \\frac{4}{55} & 0 & 0 & -\\frac{131}{220} & 0 & 0 & \\frac{6}{55} & \\frac{338}{55} \\\\\n", "{x}_{3} & \\frac{13}{7} & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 6 \\\\\n", "{x}_{2} & \\frac{4}{5} & 1 & 0 & 0 & \\frac{9}{110} & 0 & 0 & \\frac{819}{440} & 0 & 0 & -\\frac{7}{55} & \\frac{174}{55} \\\\\n", "{\\color{green}{s}}_{3} & -\\frac{2}{7} & 0 & 0 & 0 & -\\frac{2}{11} & 0 & 1 & -\\frac{117}{11} & 0 & 0 & \\frac{8}{11} & \\frac{18}{11} \\\\\n", "{\\color{green}{s}}_{2} & 1 & 0 & 0 & 0 & \\frac{1}{2} & 1 & 0 & \\frac{69}{8} & 0 & 0 & -1 & 2 \\\\\n", "{\\color{green}{s}}_{5} & \\frac{1}{5} & 0 & 0 & 0 & \\frac{23}{55} & 0 & 0 & \\frac{372}{55} & 1 & 0 & -\\frac{48}{55} & \\frac{46}{55} \\\\\n", "{\\color{green}{s}}_{6} & \\frac{3}{28} & 0 & 0 & 0 & \\frac{2}{11} & 0 & 0 & \\frac{69}{22} & 0 & 1 & -\\frac{8}{11} & \\frac{4}{11} \\\\\n", "\\hline\n", " {Z_{ind}} & -\\frac{1116}{35} & 0 & 0 & 0 & -\\frac{134}{55} & 0 & 0 & -\\frac{1917}{110} & 0 & 0 & -\\frac{36}{55} & \\frac{11158}{55}\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}_{4} & \\frac{46}{35} & 0 & 0 & 1 & \\frac{4}{55} & 0 & 0 & -\\frac{131}{220} & 0 & 0 & \\frac{6}{55} & \\frac{338}{55} \\\\\n", "{x}_{3} & \\frac{13}{7} & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 6 \\\\\n", "{x}_{2} & \\frac{4}{5} & 1 & 0 & 0 & \\frac{9}{110} & 0 & 0 & \\frac{819}{440} & 0 & 0 & -\\frac{7}{55} & \\frac{174}{55} \\\\\n", "{\\color{green}{s}}_{3} & -\\frac{2}{7} & 0 & 0 & 0 & -\\frac{2}{11} & 0 & 1 & -\\frac{117}{11} & 0 & 0 & \\frac{8}{11} & \\frac{18}{11} \\\\\n", "{\\color{green}{s}}_{2} & 1 & 0 & 0 & 0 & \\frac{1}{2} & 1 & 0 & \\frac{69}{8} & 0 & 0 & -1 & 2 \\\\\n", "{\\color{green}{s}}_{5} & \\frac{1}{5} & 0 & 0 & 0 & \\frac{23}{55} & 0 & 0 & \\frac{372}{55} & 1 & 0 & -\\frac{48}{55} & \\frac{46}{55} \\\\\n", "{\\color{green}{s}}_{6} & \\frac{3}{28} & 0 & 0 & 0 & \\frac{2}{11} & 0 & 0 & \\frac{69}{22} & 0 & 1 & -\\frac{8}{11} & \\frac{4}{11} \\\\\n", "\\hline\n", " {Z_{ind}} & -\\frac{1116}{35} & 0 & 0 & 0 & -\\frac{134}{55} & 0 & 0 & -\\frac{1917}{110} & 0 & 0 & -\\frac{36}{55} & \\frac{11158}{55}\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6 s7| rhs]\n", "[---------+-------------------------------------------------------------------------------------------------------------+---------]\n", "[ x4| 46/35 0 0 1 4/55 0 0 -131/220 0 0 6/55| 338/55]\n", "[ x3| 13/7 0 1 0 0 0 0 1 0 0 0| 6]\n", "[ x2| 4/5 1 0 0 9/110 0 0 819/440 0 0 -7/55| 174/55]\n", "[ s3| -2/7 0 0 0 -2/11 0 1 -117/11 0 0 8/11| 18/11]\n", "[ s2| 1 0 0 0 1/2 1 0 69/8 0 0 -1| 2]\n", "[ s5| 1/5 0 0 0 23/55 0 0 372/55 1 0 -48/55| 46/55]\n", "[ s6| 3/28 0 0 0 2/11 0 0 69/22 0 1 -8/11| 4/11]\n", "[---------+-------------------------------------------------------------------------------------------------------------+---------]\n", "[ Z| -1116/35 0 0 0 -134/55 0 0 -1917/110 0 0 -36/55| 11158/55]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "cambio(7,10)" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\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}_{4} & \\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{41}{42} & 0 & 0 & 0 & -\\frac{5}{1554} & -\\frac{1}{6} & 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/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}_{4} & \\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{41}{42} & 0 & 0 & 0 & -\\frac{5}{1554} & -\\frac{1}{6} & 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| -41/42 0 0 0 -5/1554 -1/6 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,[-41/42,0,0,0,-5/1554,-1/6,0,-55/42] ); R=-5/42;añadeRes(v,R) #cogemos la ecuacion de x3" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[29.395 NO NO NO 688.20 27.000 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} & {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}_{4} & 0 & 0 & 0 & 1 & \\frac{13380}{116809} & -\\frac{30}{451} & 0 & -\\frac{396}{287} & \\frac{631}{451} & \\frac{19694}{3157} \\\\\n", "{x}_{3} & 0 & 0 & 1 & 0 & -\\frac{312}{10619} & -\\frac{5}{41} & 0 & -\\frac{275}{287} & \\frac{71}{41} & \\frac{1697}{287} \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & -\\frac{30}{16687} & -\\frac{42}{451} & 0 & \\frac{11}{41} & \\frac{252}{451} & \\frac{1323}{451} \\\\\n", "{\\color{green}{s}}_{3} & 0 & 0 & 0 & 0 & \\frac{32924}{116809} & -\\frac{90}{451} & 1 & -\\frac{2090}{287} & \\frac{540}{451} & \\frac{7668}{3157} \\\\\n", "{x}_{1} & 1 & 0 & 0 & 0 & \\frac{5}{1517} & \\frac{7}{41} & 0 & \\frac{55}{41} & -\\frac{42}{41} & \\frac{5}{41} \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & 0 & 0 & -\\frac{247601}{116809} & \\frac{180}{451} & 0 & \\frac{2376}{287} & -\\frac{13257}{451} & \\frac{642226}{3157}\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}_{4} & 0 & 0 & 0 & 1 & 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"data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {b} \\\\\n", "\\hline\n", " {x}_{4} & 0 & 0 & 0 & 1 & \\frac{3345}{6956} & 0 & 0 & 0 & \\frac{4417}{752} & -\\frac{2405}{752} & 7 \\\\\n", "{x}_{3} & 0 & 0 & 1 & 0 & \\frac{62543}{97384} & 0 & 0 & \\frac{11}{7} & \\frac{44827}{4512} & -\\frac{26455}{4512} & \\frac{307}{42} \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & \\frac{3555}{6956} & 0 & 0 & \\frac{11}{5} & \\frac{5131}{752} & -\\frac{3367}{752} & 4 \\\\\n", "{\\color{green}{s}}_{3} & 0 & 0 & 0 & 0 & \\frac{67237}{48692} & 0 & 1 & -\\frac{22}{7} & \\frac{10995}{752} & -\\frac{7215}{752} & \\frac{33}{7} \\\\\n", "{x}_{1} & 1 & 0 & 0 & 0 & -\\frac{13035}{13912} & 0 & 0 & -\\frac{11}{5} & -\\frac{56441}{4512} & \\frac{37037}{4512} & 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$\\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} & \\frac{446}{869} & 0 & 0 & 1 & 0 & 0 & 0 & -\\frac{446}{395} & -\\frac{259}{474} & \\frac{481}{474} & \\frac{1436}{237} \\\\\n", "{x}_{3} & \\frac{62543}{91245} & 0 & 1 & 0 & 0 & 0 & 0 & \\frac{376}{5925} & \\frac{19351}{14220} & -\\frac{3367}{14220} & \\frac{21518}{3555} \\\\\n", "{x}_{2} & \\frac{6}{11} & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 3 \\\\\n", "{\\color{green}{s}}_{3} & \\frac{134474}{91245} & 0 & 0 & 0 & 0 & 0 & 1 & -\\frac{37832}{5925} & -\\frac{27121}{7110} & \\frac{17797}{7110} & \\frac{7154}{3555} \\\\\n", "{\\color{green}{s}}_{1} & -\\frac{13912}{13035} & 0 & 0 & 0 & 1 & 0 & 0 & \\frac{13912}{5925} & \\frac{189847}{14220} & -\\frac{124579}{14220} & 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