Chapter 4, Problem 28RP

Explanation of Solution

Optimal solution:

• The following LP example shows that it has more than one optimal solution.
• It has non degenerate basic feasible solution and there is a non-basic variable in row 0 with a zero coefficient.
• max z= $6x_1+4x_2$
• Such that
  • $x_1+2x_2\le 16$
  • $3x_1+2x_2\le 24$
  • $x_1,x_2\ge 0$
• Solving by the simplex method, the initial table is,

		$c_j$	6	4	0	0
$c_j$	$x_j$	$B_i$	$x_1$	$x_2$	$S_1$	$S_2$	Ratio $\left(\frac{B_i}{x_1}\right)$
0	$S_1$	16	1	2	1	0	16
0	$S_2$	24	3	2	0	1	8
		$z_j-c_j$	-6	-4	0	0

• Here $x_1$ is entered as it is most negative