Solve these problems using graphical linear programming and answer the questions that follow. Use
simultaneous equations to determine the optimal values of the decision variables.
a. Maximize Z = 4×1 + 3×2
Subject to
Material 6×1 + 4×2 ≤ 48 lb
Labor 4×1 + 8×2 ≤ 80 hr
x1, x2 ≥ 0
b. Maximize Z = 2×1 + 10×2
Subject to
Durability 10×1 + 4×2 ≥ 40 wk
Strength 1×1 + 6×2 ≥ 24 psi Time 1×1 + 2×2 ≤ 14 hr
x1, x2 ≥ 0
c. Maximize Z = 6A + 3B (revenue)
Subject to
Material 20A + 6B ≤ 600 lb
Machinery 25A + 20B ≤ 1,000 hr Labor 20A + 30B ≤ 1, 200 hr
A, B ≥ 0
(1) What are the optimal values of the decision variables and Z?
(2) Do any constraints have (nonzero) slack? If yes, which one(s) and how much slack does each have?
(3) Do any constraints have (nonzero) surplus? If yes, which one(s) and how much surplus does
each have?
(4) Are any constraints redundant? If yes, which one(s)? Explain briefly
