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  3. 3. solve the following linear programming problem.

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

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Advance Math

3. Solve the following linear programming problem. You must usethe dual. First write down the dual maximization LP problem, solvethat, 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 the 2nd originalconstraint changed to

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

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

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

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