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"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": [ " 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0 & 1 & 0 & 1 & 19 \\\\\n", "{\\color{green}{s}}_{3} & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 24 \\\\\n", "{x}_{1} & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 4 \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & \\frac{29}{2} & 9 & 0 & 0 & 0 & 8 & 32\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 s1 s2 s3 s4| rhs]\n", "[----+----------------------------------+----]\n", "[ s1| 0 7 2 1 0 0 4| 132]\n", "[ s2| 0 1/2 1 0 1 0 1| 19]\n", "[ s3| 0 1 1 0 0 1 1| 24]\n", "[ x1| 1 0 0 0 0 0 -1| 4]\n", "[----+----------------------------------+----]\n", "[ Z| 0 29/2 9 0 0 0 8| 32]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "cambio( 1 , 2 )\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {b} \\\\\n", "\\hline\n", " {x}_{2} & 0 & 1 & \\frac{2}{7} & \\frac{1}{7} & 0 & 0 & \\frac{4}{7} & \\frac{132}{7} \\\\\n", "{\\color{green}{s}}_{2} & 0 & 0 & \\frac{6}{7} & -\\frac{1}{14} & 1 & 0 & \\frac{5}{7} & \\frac{67}{7} \\\\\n", "{\\color{green}{s}}_{3} & 0 & 0 & \\frac{5}{7} & -\\frac{1}{7} & 0 & 1 & \\frac{3}{7} & \\frac{36}{7} \\\\\n", "{x}_{1} & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 4 \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & \\frac{34}{7} & -\\frac{29}{14} & 0 & 0 & -\\frac{2}{7} & \\frac{2138}{7}\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\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}_{2} & 0 & 1 & \\frac{2}{7} & \\frac{1}{7} & 0 & 0 & \\frac{4}{7} & \\frac{132}{7} \\\\\n", "{\\color{green}{s}}_{2} & 0 & 0 & \\frac{6}{7} & -\\frac{1}{14} & 1 & 0 & \\frac{5}{7} & \\frac{67}{7} \\\\\n", "{\\color{green}{s}}_{3} & 0 & 0 & \\frac{5}{7} & -\\frac{1}{7} & 0 & 1 & \\frac{3}{7} & \\frac{36}{7} \\\\\n", "{x}_{1} & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 4 \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & \\frac{34}{7} & -\\frac{29}{14} & 0 & 0 & -\\frac{2}{7} & \\frac{2138}{7}\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 s1 s2 s3 s4| rhs]\n", "[------+------------------------------------------------+------]\n", "[ x2| 0 1 2/7 1/7 0 0 4/7| 132/7]\n", "[ s2| 0 0 6/7 -1/14 1 0 5/7| 67/7]\n", "[ s3| 0 0 5/7 -1/7 0 1 3/7| 36/7]\n", "[ x1| 1 0 0 0 0 0 -1| 4]\n", "[------+------------------------------------------------+------]\n", "[ Z| 0 0 34/7 -29/14 0 0 -2/7|2138/7]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "cambio( 3 , 3 )\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {b} \\\\\n", "\\hline\n", " {x}_{2} & 0 & 1 & 0 & \\frac{1}{5} & 0 & -\\frac{2}{5} & \\frac{2}{5} & \\frac{84}{5} \\\\\n", "{\\color{green}{s}}_{2} & 0 & 0 & 0 & \\frac{1}{10} & 1 & -\\frac{6}{5} & \\frac{1}{5} & \\frac{17}{5} \\\\\n", "{x}_{3} & 0 & 0 & 1 & -\\frac{1}{5} & 0 & \\frac{7}{5} & \\frac{3}{5} & \\frac{36}{5} \\\\\n", "{x}_{1} & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 4 \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & 0 & -\\frac{11}{10} & 0 & -\\frac{34}{5} & -\\frac{16}{5} & \\frac{1702}{5}\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\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}_{2} & 0 & 1 & 0 & \\frac{1}{5} & 0 & -\\frac{2}{5} & \\frac{2}{5} & \\frac{84}{5} \\\\\n", "{\\color{green}{s}}_{2} & 0 & 0 & 0 & \\frac{1}{10} & 1 & -\\frac{6}{5} & \\frac{1}{5} & \\frac{17}{5} \\\\\n", "{x}_{3} & 0 & 0 & 1 & -\\frac{1}{5} & 0 & \\frac{7}{5} & \\frac{3}{5} & \\frac{36}{5} \\\\\n", "{x}_{1} & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 4 \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & 0 & -\\frac{11}{10} & 0 & -\\frac{34}{5} & -\\frac{16}{5} & \\frac{1702}{5}\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 s1 s2 s3 s4| rhs]\n", "[------+------------------------------------------------+------]\n", "[ x2| 0 1 0 1/5 0 -2/5 2/5| 84/5]\n", "[ s2| 0 0 0 1/10 1 -6/5 1/5| 17/5]\n", "[ x3| 0 0 1 -1/5 0 7/5 3/5| 36/5]\n", "[ x1| 1 0 0 0 0 0 -1| 4]\n", "[------+------------------------------------------------+------]\n", "[ Z| 0 0 0 -11/10 0 -34/5 -16/5|1702/5]" ] }, "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=3 # número de variables x's\n", "m=4 # número de restricciones (distintas de las de signo)\n", "\n", "cMP=matrix(QQ,1,m,[1.5,2,4,0] ) # coste de las materias primas\n", "\n", "\n", "A=matrix(QQ,m,n,[ # coeficientes de las variables x's\n", "[4, 7, 2],\n", "[1, 0.5, 1],\n", "[1, 1, 1],\n", "[1,0,0]\n", "])\n", "\n", "Aori=A\n", "\n", "cf=cMP*A # coste de cada unidad de producto fabricada\n", "\n", "\n", "venta=matrix(QQ,1,n,[20,30,18]) # precio de venta\n", "\n", "c=venta-cf # vector de costos (beneficio en este caso)\n", "\n", "\n", "b=matrix(QQ,m,1,[148,23,28,4]) # vector de la derecha\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", "#load('~/Jupyter/simplex2023Auto.sage')\n", "\n", "load('https://sage.unex.es/501708/simplex2023Auto.sage')\n" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "7" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "nv" ] }, { "cell_type": "code", "execution_count": 5, "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}_{2} & 0 & 1 & 0 & \\frac{1}{5} & 0 & -\\frac{2}{5} & \\frac{2}{5} & 0 & \\frac{84}{5} \\\\\n", "{\\color{green}{s}}_{2} & 0 & 0 & 0 & \\frac{1}{10} & 1 & -\\frac{6}{5} & \\frac{1}{5} & 0 & \\frac{17}{5} \\\\\n", "{x}_{3} & 0 & 0 & 1 & -\\frac{1}{5} & 0 & \\frac{7}{5} & \\frac{3}{5} & 0 & \\frac{36}{5} \\\\\n", "{x}_{1} & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 4 \\\\\n", "{\\color{green}{s}}_{5} & 0 & 0 & 0 & \\frac{1}{5} & 0 & -\\frac{2}{5} & \\frac{2}{5} & 1 & -\\frac{1}{5} \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & 0 & -\\frac{11}{10} & 0 & -\\frac{34}{5} & -\\frac{16}{5} & 0 & \\frac{1702}{5}\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}_{2} & 0 & 1 & 0 & \\frac{1}{5} & 0 & -\\frac{2}{5} & \\frac{2}{5} & 0 & \\frac{84}{5} \\\\\n", "{\\color{green}{s}}_{2} & 0 & 0 & 0 & \\frac{1}{10} & 1 & -\\frac{6}{5} & \\frac{1}{5} & 0 & \\frac{17}{5} \\\\\n", "{x}_{3} & 0 & 0 & 1 & -\\frac{1}{5} & 0 & \\frac{7}{5} & \\frac{3}{5} & 0 & \\frac{36}{5} \\\\\n", "{x}_{1} & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 4 \\\\\n", "{\\color{green}{s}}_{5} & 0 & 0 & 0 & \\frac{1}{5} & 0 & -\\frac{2}{5} & \\frac{2}{5} & 1 & -\\frac{1}{5} \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & 0 & -\\frac{11}{10} & 0 & -\\frac{34}{5} & -\\frac{16}{5} & 0 & \\frac{1702}{5}\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 s1 s2 s3 s4 s5| rhs]\n", "[------+-------------------------------------------------------+------]\n", "[ x2| 0 1 0 1/5 0 -2/5 2/5 0| 84/5]\n", "[ s2| 0 0 0 1/10 1 -6/5 1/5 0| 17/5]\n", "[ x3| 0 0 1 -1/5 0 7/5 3/5 0| 36/5]\n", "[ x1| 1 0 0 0 0 0 -1 0| 4]\n", "[ s5| 0 0 0 1/5 0 -2/5 2/5 1| -1/5]\n", "[------+-------------------------------------------------------+------]\n", "[ Z| 0 0 0 -11/10 0 -34/5 -16/5 0|1702/5]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "v=matrix(QQ,1,nv,[0,-1,0,0,0,0,0] ); R=-17\n", "añadeRes(v,R)" ] } ], "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 }