Introduction to Management Science 12th Edition by Bernard Taylor

تمرين 47

Solve the linear programming model formulated in Problem for Island Publishing Company by using the computer.
a. How much would it be worth to Island Publishing Company to obtain enough additional rack space to distribute 18,500 copies instead of the current 18,000 copies 20,000 copies
b. How much would it be worth to Island Publishing to reduce the requirement to distribute the entertainment guide from 8,000 to 7,000 copies
Problem
Island Publishing Company publishes two types of magazines on a monthly basis: a restaurant and entertainment guide and a real estate guide. The company distributes the magazines free to businesses, hotels, and stores on Hilton Head Island in South Carolina. The company's profits come exclusively from the paid advertising in the magazines. Each of the restaurant and entertainment guides 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 color photos, and accordingly it costs $0.25 per magazine to print, compared with only $0.17 for the restaurant and entertainment guide. 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 revenue.
Formulate a linear programming model for this problem.