Annie’s Barbecue Restaurant prepares two primary food items fresh each morning, pulled pork barbecue and beef brisket barbecue, which are sold as a part of different menu items, including sandwiches and barbecue plates with a variety of different sides. The maximum amount of barbecue it has ever sold in a day is 250 lbs. and the least amount is 120 lbs. It generally sells twice as much pork barbecue as beef barbecue, and as little as 20% more pork than beef. The restaurant’s meat supplier delivers 150 lbs. of pork and 110 lbs. of beef each daily. Regardless of how it is served on the menu, the restaurant makes a profit of about $8.65 per lb. of pork barbecue and $10.95 per pound for beef barbecue. The restaurant wants to know how many lbs. of each type of barbecue to cook each day in order to maximize profit.

a. Formulate and solve a linear programming model for this problem.

b. If Annie’s could get additional pork or beef from the meat supplier, which should it get? Why?

c. If the restaurant orders 10 more lbs. of beef from its supplier, how much would this increase its profit? Is this something it should do?

d. If the restaurant reduces the price of its pork BBQ menu items such that the profit from pork BBQ is $7.50 per lb., it believes it could sell two and a half times more pork than beef BBQ. Is this something they should do?