Topic 16.1: Simplex Method (Questions)

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Question 1

Maximize f(x) = x1 + 2x2 subject to:

x1 + 2x2 ≤ 3
x1 + x2 ≤ 2
x1 ≤ 1
x1 ≥ 0
x2 ≥ 0

Answer: x = (1, 1)T.

Question 2

Maximize f(x) = x1 + 2x2 subject to:

x1 + 2x2 ≤ 5
x1 + x2 ≤ 4
2x1 + x2 ≤ 6
x1 ≥ 0
x2 ≥ 0

Solution: x = (4/3, 7/3)T.

Question 3

Maximize f(x) = 2x1 + 3x2 + 2x3 subject to:

x1 + 2x2 + x3 ≤ 4
3x1 + x2 + x3 ≤ 5
x1 + x2 + 2x3 ≤ 4
x1 + x2 + x3 ≤ 3
x1 ≥ 0
x2 ≥ 0
x3 ≥ 0

Answer: x = (1,1,1)T.

Question 4

Maximize f(x) = x1 + 2x2 + x3 subject to:

x1 + 2x2 + x3 ≤ 2
3x1 + x2 + x3 ≤ 4
x1 + x2 + 2x3 ≤ 4
x1 + x2 + x3 ≤ 2
x1 ≥ 0
x2 ≥ 0
x3 ≥ 0

Solution: x = (0, 0.4, 1.2)T.

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