For the following problem, provide an objective in words, datadefinition, variable definition, and algebraic formulation (usingsummation notation when possible). You do not need to implementand solve.Submit your solution as an attached file. You may type up your workusing Microsoft Word.Hire-a-Car System rents three types of cars at two different locations. The profitcontribution made per day for each car type at each location is listed below.Car TypeLocationEconomyMid-sizeLuxuryA$25$40$10$30$35$45The management forecasts the demand per day by car type as follows:125 rentals for Economy cars, 55 rentals for Mid-size cars, and 40rentals for Luxury cars. The vehicle capacity of each location is 100 carsin location A and 120 cars in location B.

Decision Variables: Let, x11 be renting from Location A for Economy. x12 be renting from Location A…

Answered: Hire-a-Car System rents three types of…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter7: Nonlinear Optimization Models

Section: Chapter Questions

Problem 49P: If a monopolist produces q units, she can charge 400 4q dollars per unit. The variable cost is 60...

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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?
If a monopolist produces q units, she can charge 400 4q dollars per unit. The variable cost is 60 per unit. a. How can the monopolist maximize her profit? b. If the monopolist must pay a sales tax of 5% of the selling price per unit, will she increase or decrease production (relative to the situation with no sales tax)? c. Continuing part b, use SolverTable to see how a change in the sales tax affects the optimal solution. Let the sales tax vary from 0% to 8% in increments of 0.5%.
Discuss the similarities and differences between minimization and maximization problems using the graphical solution approach of Linear Programming. Be sure to provide examples. (Two-hundred words)
You have a new job as a Financial Planning assistant. Your client wants to invest money in stocks, bonds, and treasuries that have the dividend yields shown in the table below. Your job is to allocate their money across these three investments such that the total dollars of bonds plus treasuries equals the total dollars of stocks. In addition, they have identified the maximum investment in each of those three investment types (also shown below). Maximize the dividends earned. Your answer will be the total dollars to be invested in Treasuries (rounded to whole dollars). Scenario 1 Stocks: yield % 1.65 Bonds: yield % 3.04 Treasuries: yield % 1.95 Stocks: $ max 70,000 Bonds: $ max 60,000 Treasuries: $ max 25,000
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