57. A beer company has divided Bloomington intotwo territories. If the company spends x1 dollarson promotion in territory 1, it can sell 60x11y2 casesof beer there; and if it spends x2 dollars on promotion in territory 2, it can sell 40x21y2 cases of beerthere. Each case of beer sold in territory 1 sells for$10 and incurs $5 in shipping and production costs.Each case of beer sold in territory 2 sells for $9 andincurs $4 in shipping and production costs. A total of$5000 is available for promotion.a. How can the company maximize its profit?b. If an extra dollar could be spent on promotion, byapproximately how much would the company’sprofit increase? By how much would its revenueincrease?c. Use SolverTable to see how a change in the priceof beer 1 affects the optimal solution. Do the samefor a change in the price of beer 2.

57. A beer company has divided Bloomington intotwo territories. If the company spends x1 dollarson promotion in territory 1, it can sell 60x11y2 casesof beer there; and if it spends x2 dollars on promotion in territory 2, it can sell 40x21y2 cases of beerthere. Each case of beer sold in territory 1 sells for$10 and incurs $5 in shipping and production costs.Each case of beer sold in territory 2 sells for $9 andincurs $4 in shipping and production costs. A total of$5000 is available for promotion.a. How can the company maximize its profit?b. If an extra dollar could be spent on promotion, byapproximately how much would the company’sprofit increase? By how much would its revenueincrease?c. Use SolverTable to see how a change in the priceof beer 1 affects the optimal solution. Do the samefor a change in the price of beer 2.

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter7: Nonlinear Optimization Models

Section: Chapter Questions

Problem 65P

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A beer company has divided Bloomington into two territories. If the company spends x1 dollars on promotion in territory 1, it can sell 60x11/2 cases of beer there; and if it spends x2 dollars on promotionin territory 2, it can sell 40x2 1/2 cases of beer there. Each case of beer sold in territory 1 sells for $10 and incurs $5 in shipping and production costs. Each case of beer sold in territory 2 sells for $9 and incurs$4 in shipping and production costs. A total of $5000 is available for promotion.a. How can the company maximize its profit?b. If an extra dollar could be spent on promotion, by approximately how much would the company’s profit increase? By how much would its revenue increase?c. Use SolverTable to see how a change in the price of beer 1 affects the optimal solution. Do the samefor a change in the price of beer 2.
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