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Hi These Question Was Given By Our Doctor As A Homework The Course Is Operation Research And This Chapter Is

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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