FOR THIS PROBLEM: MAKE AND SOLVE A LINEAR PROGRAMMING MODEL IN EXCEL, THEN USE SENSITIVITY REPORT AND SOLVER. 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\mathrm{.}50$ per magazine in advertising revenue, whereas the real estate guide generates $$0\mathrm{.}75$ per magazine. The real estate magazine is a more sophisticated publication that includes color photos, and accordingly it costs $$0\mathrm{.}25$ per magazine to print, compared with only $$0\mathrm{.}17$ for the restaurant and entertainment guide. The publishing company has a printing budget of $$4,000$ per month. There is enough rack space to distribute at most $18,000$ magazines each month. 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 to maximize advertising revenue.

a$)$ Formulate and solve the linear programming model for this problem.

b$)$ What would be the effect on the optimal solution if the local real estate agents insisted that $12,000$ copies of the real estate guide be distributed instead of the current $8,000$ copies, or they would withdraw their advertising?

c$)$ 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?

d$)$ 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?