4. Consider the following linear programming problems:

A.

B.

Min 4x + 3×2 + 6.×3

Max

5×1 + 5×2 + 24×3

S.C.

s.t.

1x, +05x, + 1x, 2: 15

15×1 + 4×2 + 12×3 – 2800

2×2 + 1x, 2: 30

15x) + 8×2

$ 6000

1x, + 1x, + 2×3 = 20

+ 8×3 = 1200

XXX20

For each model:

a. Write the dual problem.

b. Solve the dual for problem A and the primal problem for B.

c. Use the dual solution to identify the optimal solution to the original primal problem for

A and the contrary for B.

d. Verify that the optimal values for the primal and dual problems are equal.Industrial Engineering