3. The director of advertising for a retail chain is considering how to allocate her $200,000 budget for television advertising among four programs (A, B, C, D) on three channels (1, 2, 3). Market research studies have shown that the chain's cus- tomers can be broken down into two groups: "High-end Achievers" and "Aspiring Achievers." High-end Achievers spend twice as much in the store as do Aspiring Achievers. The director wants to maximize the total in-store spending potential of the audience but must have at least three ads on each program, and cannot spend more than 50% of the budget on any one channel. The audience by pro- gram and the ad costs are: 1. Expected % High-End % Aspiring Channel Program Audience Achievers Achievers Cost/Ad 1 A 100,000 25 75 $7,500 1 B 50,000 60 40 $4,000 2 C 90,000 40 60 $6,500 3 D 80,000 50 50 $5,000 What is the most effective ad purchase ignoring the fact that the number of ads on any one program must be integer? 2. Include an integer constraint on the number of ads and re-solve. 3. Compare the two solutions.

16. Revenue with Substitutable Products. The Camera Shop sells two popular models of digital single lens reflex (DSLR) cameras. The sales of these products are not inde- pendent; if the price of one increases, the sales of the other increases. In economics. these two camera models are called substitutable products. The store wishes to estab- lish a pricing policy to maximize revenue from these products. A study of price and sales data shows the following relationships between the quantity sold (N) and price (P) of each model: NA 195 0.6PA + 0.25PB N = 301+0.08PA-0.5PB a. Construct a model for the total revenue and implement it on a spreadsheet. b. Develop a two-way data table to estimate the optimal prices for each product in order to maximize the total revenue. Vary each price from $250 to $500 in incre- ments of $10.

6. A fast-food restaurant determines that each 10¢ inc «ase in the price of a hamburger results in 25 fewer hamburgers sold. The usual price for a hamburger is $5.00 and the restaurant sells 300 hamburgers each day. a) Write an equation to model the daily revenue for the restaurant. b) Find the optimal price for a hamburger. c) What is the optimal revenue?

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