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 & # of Ads #of New Customers Reached Cost per Ad
Newspaper:1-10 900 $1,000
Newspaper:11-20 700 $900
Newspaper:21-30 400 $800
Television:1-5 10,000 $12,000
Television:6-10 7,500 $10,000
Television:11-15 5,000 $8,000
For instance, each of the first ten 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 that the company will purchase no more that 30 newspaper ads and no more than 15 television ads.
- LP Model. Your LP model must include:
1. Definition of the decision variables
2. Objective function
3. All of the constraints
a. Formulate an LP model for this problem to maximize the number of new customers reached by advertising.
B. Implement your model in a spreadsheet and sole it.
C. What is the optimal solution?
D. Suppose the number of new customers reached by 11-20 newspaper ads is 400 and the number of new customers reached by 21-30 newspaper ads is 700. Make these changes in your spreadsheet and reoptimize the problem. What is the new optimal solution? What (if anything) is wrong with this solution and why?
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