Solve these problems using graphical linear programming and answer the questions that follow. Usesimultaneous equations to determine the optimal values of the decision variables.a. Maximize Z = 4x1 + 3x2Subject toMaterial 6x1 + 4x2 ≤ 48 lbLabor 4x1 + 8x2 ≤ 80 hrx1, x2 ≥ 0 b. Maximize Z = 2x1 + 10x2Subject toDurability 10x1 + 4x2 ≥ 40 wkStrength 1x1 + 6x2 ≥ 24 psi Time 1x1 + 2x2 ≤ 14 hrx1, x2 ≥ 0 c. Maximize Z = 6A + 3B (revenue)Subject toMaterial 20A+ 6B ≤ 600 lbMachinery 25A+ 20B ≤ 1,000 hr Labor 20A+ 30B ≤ 1,200 hrA, 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 eachhave?(4) Are any constraints redundant? If yes, which one(s)? Explain briefly.
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 = 4x1 + 3x2
Subject to
Material 6x1 + 4x2 ≤ 48 lb
Labor 4x1 + 8x2 ≤ 80 hr
x1, x2 ≥ 0
b. Maximize Z = 2x1 + 10x2
Subject to
Durability 10x1 + 4x2 ≥ 40 wk
Strength 1x1 + 6x2 ≥ 24 psi Time 1x1 + 2x2 ≤ 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.
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