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SPECIAL CASES 253

l Optimal solution.
l Infeasible solution.
l Unbounded solution.
l Alternative optimal solutions.
l Degenerate solution.
For each linear programme, determine the solution situation that exists, and indicate how
you identified each situation using the Simplex method. For the problems with alternative
optimal solutions, calculate at least two optimal solutions.
17 Max 4x 1 þ 8x 2
s:t:
2x 1 þ 2x 2 10
1x 1 þ 1x 2 8
x 1 ; x 2 0

18 Min 3x 1 þ 3x 2
s:t:
2x 1 þ 0:5x 2 10
4
2x 1
4x 1 þ 4x 2 32
x 1 ; x 2 0

19 Min 1x 1 þ 1x 2
s:t:
8x 1 þ 6x 2 24
4x 1 þ 6x 2 12
2x 2 4
x 1 ; x 2 0

20 Max 2x 1 þ 1x 2 þ 1x 3
s:t:
4x 1 þ 2x 2 þ 2x 3 4
20
2x 1 þ 4x 2
4x 1 þ 8x 2 þ 2x 3 16
x 1 ; x 2 ; x 3 0

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