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 6 x 1  + 4 x 2

≤

48 lb L abor 4 x 1  + 8 x 2 ≤ 80 hr x 1 , x 2

≥

0

b. Maximize Z = 2x1 + 10x2 Subject to Durability 10 x 1  + 4 x 2

≥

40 wk Strength 1 x 1  + 6 x 2

≥

24 psi T ime 1 x 1  + 2 x 2 ≤ 14 hr x 1 , x 2

≥

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.

LO.1