A company is trying to determine how to allocate its $145,000 advertising budget

Question

A company is trying to determine how to allocate its $145,000 advertising budget for a new product. The company is considering newspaper ads and television commercials as its primary means for advertising. The following table summarizes the costs of advertising in these different media and the number of new customers reached by increasing amounts of advertising: Media & Number of Ads Number of New Cost Per Ad In Customers Reached Dollars Newspaper:1-10 Newspaper 11 -20 Newspaper: 21-30 Television: 1-5 Television: 6 10 Television: 11 15 900 700 400 10,000 7,500 5,000 1,000 900 800 12,000 10,000 8,000 For instance, each of the first 10 ads the company places in newspapers will cost $1,000 and is expected to reach 900 new customers. Each of the next 10 newspaper ads will cost $900 and is expected to reach 700 new customers. Note that the number of new customers reached by increasing amounts of advertising decreases as the advertising saturates the market. Assume the company will purchase no more than 30 newspaper ads and no more than 15 television ads. How many ads should the company place to maximize the number of new customers reached by advertising? 1. Formulate the LP model for this problem 2. Create the spreadsheet model and use Solver to

Explanation / Answer

An LP to maximize the number of new customers reached is formulated below:

Let R1 = # radio ads in 0-10 range

            R2 = # radio ads in 11-20 range

            R3 = # radio ads in 21-30 range

            T1 = # TV ads in 0-5 range

            T2 = # TV ads in 6-10 range

            T3 = # TV ads in 11-15 range

Maximize 900R1 + 700R2 + 400R3 + 10000T1 + 7500T2 + 5000T3

Subject to:

            R1 <= 10 (upper limit for type 1 radio ads)

            R2 <= 10 (upper limit for type 2 radio ads)

            R3 <= 10 (upper limit for type 3 radio ads)

            T1 <= 5 (upper limit for type 1 TV ads)

            T2 <= 5 (upper limit for type 2 TV ads)

            T3 <= 5 (upper limit for type 3 TV ads)

            R1 + R2 + R3 <= 30 (radio ads purchase limit)

            T1 + T2 + T3 <= 15 (TV ads purchase limit)

            1000R1 + 900R2 + 800R3 + 12000T1 + 10000T2 + 8000T3 <= 145000 (budget constraint)

            R1, R2, R3, T1, T2, T3 <= 0

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