Chapter 6, Problem 17RP

Explanation of Solution

To solve the given LP:

• The dual simplex table is given as follows,

z	$x_1$	$x_2$	$s_1$	$s_2$	RHS
1	2	1	0	0	0
0	-1	-1	0	1	-5
0	-1	2	1	0	-8

• Select the most negative variable as the basis variable.
• The second row is the pivot row, because the right hand side of the second constraint is the most negative.
• To choose the basis variable, calculate the ratio for the variable “${\text{x}}_{\text{j}}$” that contain the negative coefficient in the pivot row,

  $\frac{{\text{coefficient of x}}_{\text{j}}\text{at}\text{row}\text{"0"}}{{\text{coefficient of x}}_{\text{j}}\text{at}\text{pivot}\text{row}}$

• Select the entering variable that has the smallest ratio