1. A dealer wishes to purchase a number of fans and sewing machines. He has only 5760 ETB toinvest and has space for almost 20 items. A fan costs him 360 ETB and sewing machine 240 ETB.His expectation is that he can sell a fan at profit of 22 ETB and a sewing machine at a profit of18 ETB. Assuming that he can sell all the items that he can buy, how should he invest his moneyin order to maximize his profit. (Note: ETB - Ethiopian Birr)a. Formulate it as a linear programming problem (LPP)b. Use the graphical method to solve it.

Decision Variables: Suppose-X1 be the no. of fans to be purchased X2 be the no. of sewing machines…

Answered: 1. A dealer wishes to purchase a number…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter7: Nonlinear Optimization Models

Section7.3: Pricing Models

Problem 2P

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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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Xolani has just completed matric and has enrolled at a University in Cape Town, tocomplete a BCom Degree. His dad is unable to drop and fetch Xolani due to workcommitments and therefore believes it best to purchase Xolani an entry-level car, notmore than R150 000. He has given Xolani the freedom to choose and purchase thecar. Xolani has two older brothers who are car enthusiasts with lots of experience.He decides to take them along to the car dealerships. They helped him find a car thatwas safe with a fair number of additional features and style. Xolani was happy to bedriving himself to Varsity on his first day. 1 - Read the scenario above and identify examples of the following family roles. Youmay make assumptions as you see fit. Explain your answers. Initiator Influencer User Decision maker Purchaser 2 - Read the scenario above and identify examples for each phase of Xolani’s decisionmaking process, when purchasing his car.
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