Question:

The Island Publishing Company publishes two types of magazine on a monthly basis, a restaurant and entertainment guide and a real estate guide. The company distributes the magazine free to businesses, hostels, and stores on Hitlon Head Island in South Carolina. The company's profits come exclusively from the paid advertising in the magazines. Each of the restaurant and entertainment guide distributed generates $0.50 per magazine in advertising revenue, whereas the real estate guide generates $0.75 per magazine. The real estate magazine is a more sophisticated publication that includes colour photos and accordingly it costs $0.20 per magazine to print, compared with only $0.17 for the restaurant and entertainment guides. The publishing company has a printing budget of $4,000 per month. There is enough rack space to distribute at most 18,000 magazines each month. In order to entice businesses to place advertisements, Island Publishing promises to distribute at least 8,000 copies of each magazine. The company wants to determine the number of copies of each magazine it should print each month in order to maximize advertising profit.

Note: 1X = number of copies of magazine about a restaurant and entertainment guide should be printed per month, and 2X = number of copies of magazine about a real estate guide should be printed per month.

Required:

Question 1: Formulate the Linear Programing Model for this problem.

Question 2: Using the Linear Programing computer (Solver), find the company's most profitable production for each magazine per month and determine the maximization value of advertising profit.

Question 3: Based on the sensitivity report, does the company spend its all printing budget? If not, how much slack is left over?