3. A builder is developing a lakeside community. After considering possible adve

Question

3. A builder is developing a lakeside community. After considering possible advertising media and the market to be covered, the builder has decided to advertise in four media. He collected data on the number of potential customers reached, the cost per advertisement, the maximum number of advertisements available, and the exposure quality rating for each of the four media. These data are given in the following table: Maximum Number of Potential Customers Co (S) per Advertisements Quality Reached Number of Exposure Advertising Media Advertisement Available Units 3500 5200 500 1200 2500 4000 10 Daytime TV (1 min ad) Evening TV (30 sec ad) Daily newspaper (full page ad) 1700 Sunday newspaper magazine 2450 (1/2 page color ad) 75 80 45 60 18 The builder has an advertising budget of $60,000 for the campaign. In addition, he wants the following restrictions: At least 8 television commercials must be used, at least 32,000 potential customers must be reached, and no more than S12,000 may be spent on Sunday newspaper magazine advertisements. What advertising media selection plan should be recommended to maximize the total exposure quality units? Formulate a linear programming model for the above situation by determining (a) The decision variables (b) Determine the objective function. What does it represent? (c) Determine all the constraints. Briefly describe what each constraint represents. Note: Do NOT solve the problem after formulating

Explanation / Answer

No. of ads X Day time TV Y Evening TV Z Daily Newspaper A Sunday Newspaper Magazine a Decision $60,000 > = X*3500+Y*5200+Z*500+A*1200 Maximum Spend on campaign $12,000 >=A*1200 Maximum Spend on Sunday Newspaper ad 8 =Y 18 >=Z 8 >=A

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