Answer to Question #185204 in Operations Research for Vaishu

Question

Use dual simplex method to solve the following LPP .

Min z = x1 + 2x2 + 3x3

Subject to

x1 - x2 + x3 ≥ 4

x1 + x2 + 2x3 ≤ 8

x1 - x3 ≥ 2

x1, x2, x3 ≥ 0 .

Answer 1

Iteration 1$\def\arraystretch{1.0} \begin{array}{c:c:c:c:c:c:c:c:c:c:c:c:c} B& Cb &P&x_1&x_2&x_3&x_4&x_5&x_6&x_7&x_8&x_9&Q \\ \hline & & & 4 &-8&2&0&0&0&0&0&0 \\ \hdashline x_7 & 0 & 1&1&-1&1&1&0&0&1&0&0&1 \\ \hdashline x_8&0&1&-1&-1&0&0&1&0&0&1&0&-1 \\ \hdashline x_9&0&1&1&-2&-1&0&0&1&0&0&1&1 \\ \hdashline max&&0&-4&8&-2&0&0&0&0&0&0& \end{array}$