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= $6x1+4x2$

Such that

$x1+2x2≤16$

$3x1+2x2≤24$

$x1,x2≥0$

Solving by the simplex method, the initial table is,

$cj$ 6 4 0 0
$cj$ $xj$ $Bi$ $x1$ $x2$ $S1$ $S2$
Ratio

$(Bix1)$
0 $S1$ 16 1 2 1 0 16
0 $S2$ 24 3 2 0 1 8
$zj−cj$ -6 -4 0 0

Here $x1$ is entered as it is most negative

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Chapter 4, Problem 27RP

Chapter 5.1, Problem 1P

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Operations Research : Applications and Algorithms

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		$cj$	6	4	0	0
$cj$	$xj$	$Bi$	$x1$	$x2$	$S1$	$S2$	Ratio $(Bix1)$
0	$S1$	16	1	2	1	0	16
0	$S2$	24	3	2	0	1	8
		$zj−cj$	-6	-4	0	0

Solution Summary: The author explains that the following LP example shows that it has more than one optimal solution.

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