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Week 2 Extra Problems Solution

CHAPTER 2

LINEAR PROGRAMMING: BASIC CONCEPTS

Problems

2.2 a)

b) Maximize P = $600D + $300W,

subject to D ≤ 4

2W ≤ 12

3D + 2W ≤ 18

and D ≥ 0, W ≥ 0.

c) Optimal Solution = (D, W) = (x1, x2) = (4, 3). P = $3300.

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2.3 a) Optimal Solution: (D, W) = (x1, x2) = (1.67, 6.50). P = $3750.

b) Optimal Solution: (D, W) = (x1, x2) = (1.33, 7.00). P = $3900.

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c) Optimal Solution: (D, W) = (x1, x2) = (1.00, 7.50). P = $4050.

d) Each additional hour per week would increase total profit by $150.

2.5 a)

b) Let A = units of product A produced

B = units of product B produced

Maximize P = $3,000A + $2,000B,

subject to

2A + B ≤ 2

A + 2B ≤ 2

3A + 3B ≤ 4

and A ≥ 0, B ≥ 0.

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