1. Dyna Tune is trying to determine how to allocate its $145,000 advertising budget for a new product. Radio and television are the two media outlets selected for advertising. The following table shows the costs of advertising in these two media and the estimated number of new customers reached by increasing amounts of advertising.

For example, each of the first 10 ads the company places on the radio will cost $1000 and is expected to reach 900 new customers. Each of the next 10 will cost $900 and is expected to reach 700 new customers. Assume the company will purchase no more than 30 radio ads and no more than 15 television ads.

(a) Formulate an LP to maximize the number of new customers reached.

(b) Set up and solve the problem on a spreadsheet.

(c) What is the optimal solution? Explain the rationale for the solution.

(d) Suppose the number of new customers reached by 11–15 television ads is 7500 and the number reached by 6–10 ads is 5000. Resolve the problem. What is wrong with this solution? Is Solver incorrect, or is there some missing logic in the model?

2. Montana Pulp (MP) produces recycled paperboard by combining four grades of recycled paper stock. Each grade of stock has a different strength, color, and texture. The strength, color, and texture of the finished paperboard are a weighted average of those characteristics of the paper stock inputs. The table provides ...

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