Chapter 6.2, Problem 1P

Explanation of Solution

Given:

Let $x_1$ and $x_2$ be the basic variables and the analog of the LP is obtained by adding the slack variables $s_1$ and $s_2$.

$\begin{array}{l}\text{max}{\text{z=3x}}_{\text{1}}{\text{+x}}_{\text{2}}\\ {\text{subject to 2x}}_1-x_2+s_1=2\\ -x_1+x_2+s_2=4\\ x_1,x_2\ge 0\end{array}$

Writing the matrix of basic variables and vector b,

$\begin{array}{l}\text{BV=}\left\{{\text{x}}_{\text{1,}}{\text{x}}_{\text{2}}\right\}\\ \text{b=}\left[\begin{array}{l}\text{2}\\ \text{4}\end{array}\right]\end{array}$

Writing the B matrix,

$B=\left[\begin{array}{l}2-1\\ -11\end{array}\right]$

Compute the $B^{-1}$,

${\text{B}}^{\text{-1}}\text{=}\left[\begin{array}{l}\text{1}\text{1}\\ \text{1}\text{2}\end{array}\right]$

Writing $c_{Bv}$ matrix as,

$c_{Bv}{B}^{-1}=[45]$

Find the coefficient of ${\text{s}}_{\text{1}}{\text{ and s}}_{\text{2}}$ in the optimal tableau