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Unformatted text preview: 204 INTRODUCTION TOMANAGEMENTSCIENCE 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 Audience per advertisement Cost per advertisement Maximum media usage Television 100,000 $2000 10 Radio 18,000 $300 20 Newspaper 40,000 $600 10 To ensure a balanced use of advertising media, radio advertisements must not exceed 50o/C of the total number of advertisements authorized. In addition, television should account for at least 10% of the total number of advertisements authorized. a. If the promotional budget is limited to $18,200, how many commercial mes- sages should be run on each medium to maximize total audience contact? What is the allocation 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 contribution/unit Product (hours/unit) 1 2 1.00 0.35 0.30 0.20 0.20 0.50 $30.00 $15.00 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. b. In computing the profit contribution per unit, management doesn't deduct labor costs 'because the-y are conslaerea 'i\xea 'ior \'ne ,xpcomin~ 'P\aTIril1l~ 'Pm~~. 'i\~"W't'Vt'i., 'j,'\)-p- 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? PDF processed with CutePDF evaluation edition www.CutePDF.com Chapter 4 Linear Programming Applications 205 Suppose that 10, 6, and 8 hours of overtime may be scheduled in departmentsA, B, and C, respectively.The cost per hour of overtime is $18 in department A, $22.50 in department B, and $12 in department C. Formulate a linear program- ming 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 contributionto profit? How much overtime do you recommendis the revised total contributionto profit?...
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- Spring '09