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

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Advance Math

Solve the following linear programming problem. You mustuse the dual. First write down the dual maximization LP problem,solve that, then state the solution to the original minimizationproblem.

(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 the2nd original constraint changed to

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

(c) Making use of shadow costs, if the1st original constraint changed to

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

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