Min problem:

For a min problem, an LP is unbounded if there is a variable with a positive coefficient in Row 0 that has a non-positive coefficient in each constraint.

Here the optimal table is

z x1 x2 s1 s2 RHS
1 2 3 0 0 0
0 1 -1 1 0 1
0 1 -2 0 1 2

Here x₂ is as large as desired.

Since each unit by which x₂ is increased decreases z by 3 units.

Hence z is taken as small as desired...

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Chapter 4.7, Problem 4P

Chapter 4.7, Problem 6P

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Chapter 4 Solutions

Introduction to mathematical programming

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Solution Summary: The author explains that an LP is unbounded if there is a variable with positive coefficient in Row 0 that has non-positive coefficients in each constraint.

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