Linear Programming (LP) formulation:

The following example of LP is to show that it has more than one optimal solution.

It also contains nondegenerate basic feasible solution and there is 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,

c_j 6 4 0 0 Ratio
c_j x_j B_j x₁ x₂ S₁ S₂ (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 will enter as it is the greatest negative value

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Chapter 4, Problem 26RP

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		c_j	6	4	0	0	Ratio
c_j	x_j	B_j	x₁	x₂	S₁	S₂	(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 illustrates linear programming by showing that it has more than one optimal solution. The non-basic variable in row 0 has a zero coefficient.

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