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Consider the following optimization problem: “Consider the ellipse given by . If you inscribe a rectangle in this ellipse, what are the dimensions of the rectangle that maximize its area? What is the maximum area?” Without actually solving the problem, detail the steps you would take if you were asked to solve the problem (say on an exam or homework). In other words, walk through the problem so you demonstrate an understanding of how you would go about finding the dimensions of the rectangle that maximize its area and the maximum area.

Practical Management Science

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter4: Linear Programming Models

Section: Chapter Questions

Problem 64P

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Consider the following optimization problem: “Consider the ellipse given by

. If you inscribe a rectangle in this ellipse, what are the dimensions of the rectangle that maximize its area? What is the maximum area?”

Without actually solving the problem, detail the steps you would take if you were asked to solve the problem (say on an exam or homework). In other words, walk through the problem so you demonstrate an understanding of how you would go about finding the dimensions of the rectangle that maximize its area and the maximum area.

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Seas Beginning sells clothing by mail order. An important question is when to strike a customer from the companys mailing list. At present, the company strikes a customer from its mailing list if a customer fails to order from six consecutive catalogs. The company wants to know whether striking a customer from its list after a customer fails to order from four consecutive catalogs results in a higher profit per customer. The following data are available: If a customer placed an order the last time she received a catalog, then there is a 20% chance she will order from the next catalog. If a customer last placed an order one catalog ago, there is a 16% chance she will order from the next catalog she receives. If a customer last placed an order two catalogs ago, there is a 12% chance she will order from the next catalog she receives. If a customer last placed an order three catalogs ago, there is an 8% chance she will order from the next catalog she receives. If a customer last placed an order four catalogs ago, there is a 4% chance she will order from the next catalog she receives. If a customer last placed an order five catalogs ago, there is a 2% chance she will order from the next catalog she receives. It costs 2 to send a catalog, and the average profit per order is 30. Assume a customer has just placed an order. To maximize expected profit per customer, would Seas Beginning make more money canceling such a customer after six nonorders or four nonorders?

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