Question

In: Advanced Math

3. Solve the following linear programming problem. You must use the dual. First write down the...

3. Solve the following linear programming problem. You must use the dual. First write down the dual maximization LP problem, solve that, then state the solution to the original minimization problem.

(a) Minimize w = 4y1 + 5y2 + 7y3

Subject to: y1 + y2 + y3 ≥ 18

2y1 + y2 + 2y3 ≥ 20

y1 + 2y2 + 3y3 ≥ 25

y1, y2, y3 ≥ 0

(b) Making use of shadow costs, if the 2nd original constraint changed to

2y1 + y2 + 2y3 ≥ 24, now what will the minimum of w be? Explain clearly.

(c) Making use of shadow costs, if the 1st original constraint changed to

y1 + y2 + y3 21, now what will the minimum of w be? Explain clearly.

Solutions

Expert Solution

Colby Messinger answered 1 year ago
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