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"stdout", "output_type": "stream", "text": [ "cambio( 3 , 3 )\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {b} \\\\\n", "\\hline\n", " {x}_{2} & 0 & 1 & 0 & \\frac{3}{5} & -\\frac{1}{5} & \\frac{3}{5} & 128 \\\\\n", "{x}_{1} & 1 & 0 & 0 & -\\frac{1}{5} & \\frac{2}{5} & -\\frac{1}{5} & 74 \\\\\n", "{x}_{3} & 0 & 0 & 1 & 0 & 0 & 1 & 10 \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & 0 & -\\frac{26}{5} & -\\frac{8}{5} & -\\frac{16}{5} & 2256\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {b} \\\\\n", "\\hline\n", " {x}_{2} & 0 & 1 & 0 & \\frac{3}{5} & -\\frac{1}{5} & \\frac{3}{5} & 128 \\\\\n", "{x}_{1} & 1 & 0 & 0 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"b=matrix(QQ,m,1,[320,350,10]) # vector de la derecha\n", "\n", "\n", "######################################################\n", "############### VARIABLES DE HOLGURA ################\n", "\n", "\n", "h=matrix(ZZ,1,m,[1,1,1]) # variables de holgura: \n", " # Pon 1 si va sumando, \n", " # -1 si va restando y \n", " # 0 si no hay variable de holgura.\n", "\n", "\n", "\n", "\n", "####################################################################\n", "############ HASTA AQUÍ LOS DATOS ################################\n", "####################################################################\n", "\n", "load('https://sage.unex.es/501708/simplex2023Auto.sage')\n", "\n" ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {b} \\\\\n", "\\hline\n", " {x}_{2} & 0 & 1 & 0 & \\frac{3}{5} & -\\frac{1}{5} & \\frac{3}{5} & 128 \\\\\n", "{x}_{1} & 1 & 0 & 0 & -\\frac{1}{5} & \\frac{2}{5} & -\\frac{1}{5} & 74 \\\\\n", "{x}_{3} & 0 & 0 & 1 & 0 & 0 & 1 & 10 \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & 0 & -\\frac{26}{5} & -\\frac{8}{5} & -\\frac{16}{5} & 2256 \\\\\n", "{Z{1p}} & 0 & 0 & 0 & 0 & 0 & 1 & -10\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\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}_{2} & 0 & 1 & 0 & \\frac{3}{5} & -\\frac{1}{5} & \\frac{3}{5} & 128 \\\\\n", "{x}_{1} & 1 & 0 & 0 & -\\frac{1}{5} & \\frac{2}{5} & -\\frac{1}{5} & 74 \\\\\n", "{x}_{3} & 0 & 0 & 1 & 0 & 0 & 1 & 10 \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & 0 & -\\frac{26}{5} & -\\frac{8}{5} & -\\frac{16}{5} & 2256 \\\\\n", "{Z{1p}} & 0 & 0 & 0 & 0 & 0 & 1 & -10\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 s1 s2 s3| rhs]\n", "[-----+-----------------------------------+-----]\n", "[ x2| 0 1 0 3/5 -1/5 3/5| 128]\n", "[ x1| 1 0 0 -1/5 2/5 -1/5| 74]\n", "[ x3| 0 0 1 0 0 1| 10]\n", "[-----+-----------------------------------+-----]\n", "[ Z| 0 0 0 -26/5 -8/5 -16/5| 2256]\n", "[ Z1p| 0 0 0 0 0 1| -10]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "cp=matrix(QQ,1,n,[0,0,-1] ) ; param1c(cp)" ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrr|rrr}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {b} & {b_1} & {b_2} \\\\\n", "\\hline\n", " {x}_{2} & 0 & 1 & 0 & \\frac{3}{5} & -\\frac{1}{5} & \\frac{3}{5} & 128 & \\frac{3}{5} & \\frac{3}{5} \\\\\n", "{x}_{1} & 1 & 0 & 0 & -\\frac{1}{5} & \\frac{2}{5} & -\\frac{1}{5} & 74 & -\\frac{1}{5} & -\\frac{1}{5} \\\\\n", "{x}_{3} & 0 & 0 & 1 & 0 & 0 & 1 & 10 & 0 & 1 \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & 0 & -\\frac{26}{5} & -\\frac{8}{5} & -\\frac{16}{5} & 2256 & \\frac{26}{5} & \\frac{16}{5} \\\\\n", "{Z{1p}} & 0 & 0 & 0 & 0 & 0 & 1 & -10 & 0 & -1\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrr|rrr}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {b} & {b_1} & {b_2} \\\\\n", "\\hline\n", " {x}_{2} & 0 & 1 & 0 & \\frac{3}{5} & -\\frac{1}{5} & \\frac{3}{5} & 128 & \\frac{3}{5} & \\frac{3}{5} \\\\\n", "{x}_{1} & 1 & 0 & 0 & -\\frac{1}{5} & \\frac{2}{5} & -\\frac{1}{5} & 74 & -\\frac{1}{5} & -\\frac{1}{5} \\\\\n", "{x}_{3} & 0 & 0 & 1 & 0 & 0 & 1 & 10 & 0 & 1 \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & 0 & -\\frac{26}{5} & -\\frac{8}{5} & -\\frac{16}{5} & 2256 & \\frac{26}{5} & \\frac{16}{5} \\\\\n", "{Z{1p}} & 0 & 0 & 0 & 0 & 0 & 1 & -10 & 0 & -1\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 s1 s2 s3| rhs rhs1 rhs2]\n", "[-----+-----------------------------------+-----------------]\n", "[ x2| 0 1 0 3/5 -1/5 3/5| 128 3/5 3/5]\n", "[ x1| 1 0 0 -1/5 2/5 -1/5| 74 -1/5 -1/5]\n", "[ x3| 0 0 1 0 0 1| 10 0 1]\n", "[-----+-----------------------------------+-----------------]\n", "[ Z| 0 0 0 -26/5 -8/5 -16/5| 2256 26/5 16/5]\n", "[ Z1p| 0 0 0 0 0 1| -10 0 -1]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "b1p=matrix(QQ,m,1,[1,0,0]); b2p=matrix(QQ,m,1,[0,0,1]); param2b(b1p,b2p)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Si llamamos $\\mu$ al parámetro que mueve el precio de la hora extra, qué ocurriría si $\\mu >16/5$?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " " ] }, { "cell_type": "code", "execution_count": 36, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrr|rrr}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {b} & {b_1} & {b_2} \\\\\n", "\\hline\n", " {x}_{2} & 0 & 1 & -\\frac{3}{5} & \\frac{3}{5} & -\\frac{1}{5} & 0 & 122 & \\frac{3}{5} & 0 \\\\\n", "{x}_{1} & 1 & 0 & \\frac{1}{5} & -\\frac{1}{5} & \\frac{2}{5} & 0 & 76 & -\\frac{1}{5} & 0 \\\\\n", "{\\color{green}{s}}_{3} & 0 & 0 & 1 & 0 & 0 & 1 & 10 & 0 & 1 \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & \\frac{16}{5} & -\\frac{26}{5} & -\\frac{8}{5} & 0 & 2224 & \\frac{26}{5} & 0 \\\\\n", "{Z{1p}} & 0 & 0 & -1 & 0 & 0 & 0 & 0 & 0 & 0\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrr|rrr}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {b} & {b_1} & {b_2} \\\\\n", "\\hline\n", " {x}_{2} & 0 & 1 & -\\frac{3}{5} & \\frac{3}{5} & -\\frac{1}{5} & 0 & 122 & \\frac{3}{5} & 0 \\\\\n", "{x}_{1} & 1 & 0 & \\frac{1}{5} & -\\frac{1}{5} & \\frac{2}{5} & 0 & 76 & -\\frac{1}{5} & 0 \\\\\n", "{\\color{green}{s}}_{3} & 0 & 0 & 1 & 0 & 0 & 1 & 10 & 0 & 1 \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & \\frac{16}{5} & -\\frac{26}{5} & -\\frac{8}{5} & 0 & 2224 & \\frac{26}{5} & 0 \\\\\n", "{Z{1p}} & 0 & 0 & -1 & 0 & 0 & 0 & 0 & 0 & 0\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 s1 s2 s3| rhs rhs1 rhs2]\n", "[-----+-----------------------------------+-----------------]\n", "[ x2| 0 1 -3/5 3/5 -1/5 0| 122 3/5 0]\n", "[ x1| 1 0 1/5 -1/5 2/5 0| 76 -1/5 0]\n", "[ s3| 0 0 1 0 0 1| 10 0 1]\n", "[-----+-----------------------------------+-----------------]\n", "[ Z| 0 0 16/5 -26/5 -8/5 0| 2224 26/5 0]\n", "[ Z1p| 0 0 -1 0 0 0| 0 0 0]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "cambio(3,6)" ] } ], "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 }