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coeficientes de las variables x's\n", "[2,2,1,2,-1,1],\n", "[1,5,-1,-1,1,-1],\n", "[-1,3,2,-2,-1,1]\n", "])\n", "\n", "b=matrix(QQ,m,1,[10,15,25]) # vector de la derecha\n", "\n", "\n", "h=matrix(ZZ,1,m,[0,0,0]) # 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", "t=matrix(ZZ,1,m,[1,1,1]) # variables artificiales: \n", " # pon 1 si utilizas variable artificial en la fila i-ésima\n", " # 0 si no utilizas variable artificial en la fila i-ésima\n", "\n", "colId=(7,8,9) # posición de la matriz identidad\n", "\n", "\n", " \n", " \n", "####################################################################\n", "############ HASTA AQUÍ LOS DATOS ################################\n", "####################################################################\n", "\n", "\n", "\n", "\n", "load('https://sage.unex.es/501708/simplex2023CompletamenteManual.sage')" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[2.8571]\n", "[ NO]\n", "[ NO]" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "cocientes(6)" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "scrolled": false }, "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} & {x}_{5} & {x}_{6} & {\\color{red}{t}}_{1} & {\\color{red}{t}}_{2} & {\\color{red}{t}}_{3} & {b} \\\\\n", "\\hline\n", " {\\color{red}{t}}_{1} & \\frac{8}{5} & 0 & \\frac{7}{5} & \\frac{12}{5} & -\\frac{7}{5} & \\frac{7}{5} & 1 & -\\frac{2}{5} & 0 & 4 \\\\\n", "{x}_{2} & \\frac{1}{5} & 1 & -\\frac{1}{5} & -\\frac{1}{5} & \\frac{1}{5} & -\\frac{1}{5} & 0 & \\frac{1}{5} & 0 & 3 \\\\\n", "{\\color{red}{t}}_{3} & -\\frac{8}{5} & 0 & \\frac{13}{5} & -\\frac{7}{5} & -\\frac{8}{5} & \\frac{8}{5} & 0 & -\\frac{3}{5} & 1 & 16 \\\\\n", "\\hline\n", " {W_{ind}} & 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-7/5 7/5 1 -2/5 0| 4]\n", "[ x2| 1/5 1 -1/5 -1/5 1/5 -1/5 0 1/5 0| 3]\n", "[ t3|-8/5 0 13/5 -7/5 -8/5 8/5 0 -3/5 1| 16]\n", "[----+--------------------------------------------+----]\n", "[ W| 0 0 -4 -1 3 -3 0 2 0| 20]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "cambio(2,2)" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {x}_{5} & {x}_{6} & {\\color{red}{t}}_{1} & {\\color{red}{t}}_{2} & {\\color{red}{t}}_{3} & {b} \\\\\n", "\\hline\n", " {x}_{3} & \\frac{8}{7} & 0 & 1 & \\frac{12}{7} & -1 & 1 & \\frac{5}{7} & -\\frac{2}{7} & 0 & \\frac{20}{7} \\\\\n", "{x}_{2} & \\frac{3}{7} & 1 & 0 & \\frac{1}{7} & 0 & 0 & \\frac{1}{7} & \\frac{1}{7} & 0 & \\frac{25}{7} \\\\\n", "{\\color{red}{t}}_{3} & -\\frac{32}{7} & 0 & 0 & -\\frac{41}{7} & 1 & -1 & -\\frac{13}{7} & \\frac{1}{7} & 1 & \\frac{60}{7} \\\\\n", "\\hline\n", " {W_{ind}} & \\frac{32}{7} & 0 & 0 & \\frac{41}{7} & -1 & 1 & \\frac{20}{7} & \\frac{6}{7} & 0 & \\frac{60}{7}\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {x}_{5} & {x}_{6} & {\\color{red}{t}}_{1} & {\\color{red}{t}}_{2} & {\\color{red}{t}}_{3} & {b} \\\\\n", "\\hline\n", " {x}_{3} & \\frac{8}{7} & 0 & 1 & \\frac{12}{7} & -1 & 1 & \\frac{5}{7} & -\\frac{2}{7} & 0 & \\frac{20}{7} \\\\\n", "{x}_{2} & \\frac{3}{7} & 1 & 0 & \\frac{1}{7} & 0 & 0 & \\frac{1}{7} & \\frac{1}{7} & 0 & \\frac{25}{7} \\\\\n", "{\\color{red}{t}}_{3} & -\\frac{32}{7} & 0 & 0 & -\\frac{41}{7} & 1 & -1 & -\\frac{13}{7} & \\frac{1}{7} & 1 & \\frac{60}{7} \\\\\n", "\\hline\n", " {W_{ind}} & \\frac{32}{7} & 0 & 0 & \\frac{41}{7} & -1 & 1 & \\frac{20}{7} & \\frac{6}{7} & 0 & \\frac{60}{7}\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 x5 x6 t1 t2 t3| rhs]\n", "[-----+-----------------------------------------------------+-----]\n", "[ x3| 8/7 0 1 12/7 -1 1 5/7 -2/7 0| 20/7]\n", "[ x2| 3/7 1 0 1/7 0 0 1/7 1/7 0| 25/7]\n", "[ t3|-32/7 0 0 -41/7 1 -1 -13/7 1/7 1| 60/7]\n", "[-----+-----------------------------------------------------+-----]\n", "[ W| 32/7 0 0 41/7 -1 1 20/7 6/7 0| 60/7]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "cambio(1,3)" ] }, { "cell_type": "code", "execution_count": 21, "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} & {x}_{5} & {x}_{6} & {\\color{red}{t}}_{1} & {\\color{red}{t}}_{2} & {\\color{red}{t}}_{3} & {b} \\\\\n", "\\hline\n", " {x}_{3} & -\\frac{24}{7} & 0 & 1 & -\\frac{29}{7} & 0 & 0 & -\\frac{8}{7} & -\\frac{1}{7} & 1 & \\frac{80}{7} \\\\\n", "{x}_{2} & \\frac{3}{7} & 1 & 0 & \\frac{1}{7} & 0 & 0 & \\frac{1}{7} & 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