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3. Consider the following problem. Maximize Z = 2x1 + 7x2 + 4x3 subject to x1 + 2x2 + x3 ≤ 10 3x1 + 3x2 + 2x3 ≤ 10 x1, x2, x3 ≥ 0. 1 (a) (points: 4) Construct the dual problem for this primal problem. (b) (points: 2) Use the dual problem to demonstrate that the optimal value of Z for the primal problem cannot exceed 25.

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Answer:

answer is the attachment below:

Step-by-step explanation:

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Answer:

Step-by-step explanation:

Question a. Construct a dual problem for this primal problem

Solution:

Minimize W=10y1+10y2

Y1+3Y2≥3

2Y1+3Y2≥7

Y1+2Y2≥4

Y1≥0,Y2≥0

Question b. Use the dual problem to demonstrate that the optimal value of Z for the primal problem cannot exceed 25.

Solution.

The solution (0,2.5) gives W=25 and given how Z W then Z can not be greater than 25.

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