Chapter 6.7, Problem 3P

Explanation of Solution

Determining optimal z-value for the LP:

Maximize, $z=-x_1+5x_2$

Subject to the constraints,

$\begin{array}{c}{x}_1+2x_2\le 0.5\\ -x_1+3x_2\le 0.5\end{array}$

And $x_1,x_2\ge 0$

LPP after converting to the standard form:

Maximize, $Z=-x_1+5x_2+0S_1+0S_2$

Subject to the constraints,

$\begin{array}{c}{x}_1+2x_2+1S_1+0S_2=0.5\\ -x_1+3x_2+0S_1+1S_2=0.5\end{array}$

And $x_1,x_2,S_1,S_2\ge 0$

Forming the initial simplex table and continuing with the problem

Iteration 1:

			-1	5	0	0
$Y_B$	$Y_B$	${\text{X}}_{\text{B}}$	$x_2$	$x_2$	${\text{S}}_{\text{1}}$	${\text{S}}_2$	$\min ({\text{X}}_{\text{B}}/x_2)$
0	${\text{S}}_{\text{1}}$	0.5	1	2	1	0	$0.5/2=0.25$
0	${\text{S}}_2$	0.5	-1	3	0	1	$0.5/3=0$