Solve these problems using graphical linear programming and then answer the questions that follow.

Use simultaneous equations to determine the optimal values of the decision variables.

a. Minimize Z = 1.80S + 2.20T Subject to:

Potassium 5S + 8T

≥

200 gr Carbohydrate 15S + 6T

≥

240 gr Protein 4S + 12T ≥ 180 gr T

T

≥

10 gr S, T

≥

0

b. Minimize Z = 2x1 + 3x2 Subject to:

D 4 x 1  + 2 x 2

≥

20 E

2 x 1  + 6 x 2

≥

18 F 1 x 1  + 2 x 2 ≤ 12 x 1 , x 2

≥

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