minimize_lp(10*x1 + 15*x2 + 20*x3,[[br]2*x1 + x2 >= 2,[br]-x1 + 2*x3 >= -3,[br]3*x2 - 2*x3 >= 5]), [color=#0000ff]nonegative_lp=true;[/color][br][br][math]\textcolor{blue}{\large\mathcal{Maxima-Link}\nearrow[/math] [br]https://sagecell.sagemath.org/?q=mdehdz[br] [br]Tablo:={2 * x1 + x2 = 2, -x1 + 2 * x3 = -3, 3 * x2 - 2 * x3 = 5, 10 * x1 + 15 * x2 + 20 * x3 = 0}[br]Dualer Simplex to min with max-programm[br][i][br][color=#0000ff]nonegative_lp=true; x1,x2,x3>0 [/color][/i][br][math]Start \, := \, \left(\begin{array}{rrrrrrr}2&-1&0&1&0&0&10\\1&0&3&0&1&0&15\\0&2&-2&0&0&1&20\\-2&3&-5&0&0&0&0\\\end{array}\right),PV0 \, := \, \left\{ 2, 3 \right\} [/math][br] [math]A_1 \, := \, \left(\begin{array}{rrrrrrr}2&-1&0&1&0&0&10\\\frac{1}{3}&0&1&0&\frac{1}{3}&0&5\\\frac{2}{3}&2&0&0&\frac{2}{3}&1&30\\\frac{-1}{3}&3&0&0&\frac{5}{3}&0&25\\\end{array}\right), PV1 \, := \, \left\{ 1, 1 \right\}[/math][br] [math]A_2 \, := \, \left(\begin{array}{rrrrrrr}1&\frac{-1}{2}&0&\frac{1}{2}&0&0&5\\0&\frac{1}{6}&1&\frac{-1}{6}&\frac{1}{3}&0&\frac{10}{3}\\0&\frac{7}{3}&0&\frac{-1}{3}&\frac{2}{3}&1&\frac{80}{3}\\0&\frac{17}{6}&0&\frac{1}{6}&\frac{5}{3}&0&\frac{80}{3}\\\end{array}\right) [/math][br] [math]IL \, := \, \left(\begin{array}{r}\frac{1}{6}\\\frac{5}{3}\\0\\\end{array}\right)[/math][br][color=#0000ff][color=#0000ff][i]nonegative_lp=false; x1,x2,x3<=>0[/i][/color][br] [math]PV2 \, := \, \left\{ 3, 2 \right\}, \text{weiter per Handeingabe um auch neg. Lösung zu finden}[/math][br] [math]A_3 \, := \, \left(\begin{array}{rrrrrrr}1&0&0&\frac{3}{7}&\frac{1}{7}&\frac{3}{14}&\frac{75}{7}\\0&0&1&\frac{-1}{7}&\frac{2}{7}&\frac{-1}{14}&\frac{10}{7}\\0&1&0&\frac{-1}{7}&\frac{2}{7}&\frac{3}{7}&\frac{80}{7}\\0&0&0&\frac{4}{7}&\frac{6}{7}&\frac{-17}{14}&\frac{-40}{7}\\\end{array}\right)[/math][br] [math]IL \, := \, \left(\begin{array}{r}\frac{4}{7}\\\frac{6}{7}\\\frac{-17}{14}\\\end{array}\right)[/math][br][/color][br][br][math]\textcolor{blue}{\large\mathcal{Maxima-Link}\nearrow[/math] [br]https://sagecell.sagemath.org/?q=ttjcts[br][br]Zuschnitt-Optimierung[math]\nearrow[/math][br]https://www.zingel.de/pdf/08sim.pdf