The Royal Seas Company runs a three-night cruise to the Caribbean from Port Canaveral. The company wants to run TV ads promoting its cruises to high-income men, high-income women, and retirees. The company has decided to consider airing ads during prime time, afternoon soap operas, and the evening news. The number of exposures (in millions) expected to be generated by each type of ad in each of the company’s target audiences is summarized in the following table: Prime Time Soap Operas Evening News
High-income men 6 3 6
High-income women 3 4 4
Retirees 4 7 3

Ads during prime time, the afternoon soaps, and the news hour cost $120,000, $85,000, and $100,000, respectively. Royal Seas wants to achieve the following goals:

Goal 1: Spend approximately $900,000 on TV advertising.
Goal 2: Generate approximately 45 million exposures among high-income men.
Goal 3: Generate approximately 60 million exposures among high-income women.
Goal 4: Generate approximately 50 million exposures among retirees.

Required:
a. Formulate a GP model for this problem. Assume overachievement of the first goal is equally as undesirable as underachievement of the remaining goals on a percentage deviation basis.
b. Implement your model in a spreadsheet and solve it.
c. What is the optimal solution?
d. What solution allows the company to spend as close to $900,000 as possible without exceeding this amount?
e. Assume that the company can spend no more than $900,000. What solution minimizes the maximum percentage underachievement of all the goals?
f. Which of the two preceding solutions would you most prefer? Why?