C04 LP 12ed

C04 LP 12ed - PROBLEMS Note: The following problems have...

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PROBLEMS Note: The following problems have been designed to give you an understanding and apprecia- tion of the broad range of problems that can be formulated as linear programs. You should be able to formulate a linear programming model for each of the problems. However, you will need access to a linear programming computer package to develop the solutions and make the re- quested interpretations. 1. The Westchester Chamber of Commerce periodically sponsors public service seminars and programs. Currently, promotional plans are under way for this year's program. Advertis- ing alternatives include television, radio, and newspaper. Audience estimates, costs, and maximum media usage limitations are as shown. Constraint Television Radio Newspaper Audience per advertisement 100,000 1 8,000 40,000 Cost per advertisement $2000 $300 $600 Maximum media usage 10 20 10 To ensure a balanced use of advertising media, radio advertisements must not exceed 50% of the total number of advertisements authorized. In addition, television should account for at least 10% of the total number of advertisements authorized.
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Problems 195 a. If the promotional budget is limited to $18,200, how many commercial messages should be run on each medium to maximize total audience contact? What is the allo- cation of the budget among the three media, and what is the total audience reached? b. By how much would audience contact increase if an extra $100 were allocated to the / promotional budget? 2. The management of Hartman Company is trying to determine the amount of each of two products to produce over the coming planning period. The following information concerns labor availability, labor utilization, and product profitability. Department A B C Profit contributionlunit Product (hoursfunit) Labor-Hours Available 100 36 50 a. Develop a linear programming model of the Hartman Company problem. Solve the model to determine the optimal production quantities of products 1 and 2. In computing the profit contribution per unit, management doesn't deduct labor costs because they are considered fixed for the upcoming planning period. However, sup- pose that overtime can be scheduled in some of the departments. Which departments would you recommend scheduling for overtime? How much would you be willing to pay per hour of overtime in each department? c. Suppose that 10,6, and 8 hours of overtime may be scheduled in departments A, B, and C, respectively. The cost per hour of overtime is $18 in department A, $22.50 in de- partment B, and $12 in department C. Formulate a linear programming model that can be used to determine the optimal production quantities if overtime is made available. What are the optimal production quantities, and what is the revised total contribution to profit? How much overtime do you recommend using in each department? What is the increase in the total contribution to profit if overtime is used?
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This note was uploaded on 03/07/2010 for the course MATH 2310 taught by Professor Shakroh during the Spring '09 term at Langara.

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C04 LP 12ed - PROBLEMS Note: The following problems have...

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