Problems 6 1. The Westchester Chamber of Commerce periodically sponsor public service seminars and programs. Currently, promotional plans are under way for this year’s program. Advertising alternatives include television, radio, and news paper. Audience estimates, cost, and maximum media usage limitations are shown. Constraint Television Radio Newspaper Audience per advertisement 100,000 18,000 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. 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 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. Ajax Fuels Inc. is developing a new additive for air plane fuels. The additive is mixture of three ingredients: A, B, and C. For proper performance, the total amount of additive (amount of A + amount of B + amount of C) must be at least 10 ounces per gallon of fuel. However, because of safety reason, the amount of additive must not exceed 15 ounces per gallon of fuel. The mix or blend of the three ingredients is critical. At least 1 ounce of ingredient A must be used for every ounce of ingredient B. The amount of ingredient C must be used for every ounce of ingredient A. If the costs per ounce for ingredients A,B, and C are $0.10, $0.03, and 0.09, respectively, find the minimum cost mixture A,B, and C for each gallon of airplane fuel. 3. As part of the settlement for a class action lawsuit, How worth Corporation must provide sufficient cash to make the following annual payment (in thousand dollars) Year 1 2 3 4 5 6 Payment 190 215 240 285 315 400 The annual payments must be made at the beginning of each year. The judge will approve an amount that, along with earning on its investment, will cover the annual payments. Investment of the fund will be limited to savings (at 4% annually) and government securities, at price and rates currently quoted in The Wall Street Journal. Horxworth wants to develop a plan for making the annual payments by investing in the following securities (par value=$1000). Funds not invested in three securities will be placed in saving Assume that interest is paid annually. The plan will be submitted to the judge and, if approved. Horxworth will be required to pay trustee the amount that will be required to fund the plan. Security 1 2 Current Price $1055 $1000 Rate (%) 6.750 5.125 Year to maturity 3 4 a. Use the linear programming to find the minimum cash settlement necessary to fund the annual payments. b. Use the dual price to determine how much more Horxworth should be willing to pay now to reduce the payment at the beginning of year 6 to $400,000. c. Use the dual price to determine how much more Horxworth should be willing to pay to reduce the year 1 payment to $150,000. d. Suppose that the annual payments are to be made at the end of each year. Reformulate the model to accommodate this change. How much would Horxworth save if this change could be negotiated?