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

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 2^nd 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 1^st original constraint changed to

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

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Expert Solution

Colby Messinger answered 2 months ago

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