Max 50X + 40YSubject to:X + Y >= 5X-3Y <= 010X +15Y <= 15020X + 10Y <= 16030X + 10Y >= 135X, Y >= 0Answer the following Questions:(Constraint #1)(Constraint #2)(Constraint #3)(Constraint #4)(Constraint #5)a) Does an optimal solution exist? If so, what is the optimal solution? If not, why does not anoptimal solution exist? Show your calculations and answers clearly.b) Does constraint #5 have slack or surplus? If so, which one and how much?c) Up to how much can the coefficient of Y in the objective function increase without changingthe optimal solution? Show your calculations and answers clearly.d) If one increases the righthand side value of constraint #2 by 2, by how much does the valueof the objective function change, compared with that at the original optimal solution? Showyour calculations and answers clearly.e) Up to how much can the righthand side value of constraint #1 be increased withoutchanging the dual value (i.e., the shadow price) of constraint #1? Answers clearly anddescribe reasons.f) If one increases the righthand side value of constraint #3 by 1, by how much does the valueof the objective function change, compared with that at the original optimal solution? Showyour calculations and answers clearly.

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Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

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Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...

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