QUESTION 1The Brown family owns 420 acres of farmland in North Carolina on whichthey grow corn and tobacco. Each acre of corn costs $120 to plant,cultivate, and harvest; each acre of tobacco costs $240. They have abudget of $60,000 for next year. The government limits the number ofacres of tobacco that can be planted to 150. The profit from each acre ofcorn is $300; the profit from each acre of tobacco is $450. They want toknow how many acres of each crop to plant to maximize their profit.They have an opportunity to lease some extra land from a neighbor. Theneighbor is offering the land to them for $160 per acre. Based on thesensitivity analysis, you may suggest that the family the land at thatprice because the maximum price the Browns should pay their neighborfor the land isshould not lease; $150should lease; $160should lease; $450may lease; $80none of the above

Let acres of corn produced be x1 and tobacco produced be x2 The objective is to maximize the profit.…

Answered: QUESTION 1 The Brown family owns 420…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter7: Nonlinear Optimization Models

Section7.3: Pricing Models

Problem 3P: Pricing Decisions at Madison The Madison Company manufactures and retails a certain product. The...

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Pricing Decisions at Madison The Madison Company manufactures and retails a certain product. The company wants to determine the price that maximizes its profit from this product. The unit cost of producing and marketing the product is 50. Madison will certainly charge at least 50 for the product to ensure that it makes some profit. However, there is a very competitive market for this product, so that Madisons demand falls sharply when it increases its price. How should the company proceed?2 In the pricing model in Example 7.1 with the constant elasticity demand function, the assumption is that all units demanded are sold. Suppose the company has the capacity to produce only 200 units. If demand is less than capacity, all of demand is sold. If demand is greater than or equal to capacity, only 200 units are sold. Use Solver to find the optimal price and the corresponding profit. Then use SolverTable to see how sensitive these answers are to the production capacity, letting it vary from 170 to 230 in increments of 10. Discuss your findings relative to the original solution in Example 7.1. In other words, what is the effect of capacity on the optimal price and profit?
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