Prissy Pauline’s Barbecue Restaurant in Greensboro makes two primary food items fresh each morning: pulled pork barbecue and beef brisket barbecue. These two items are sold as part of different menu items, including sandwich and barbecue plates, with a variety of different sides. The maximum amount of barbecue Prissy Pauline’s has ever sold in a day is 250 pounds, and the least amount is 120 pounds. It generally sells more pork barbecue than beef barbecue—as much as twice as much pork as beef barbecue, and as little as 20% more pork than beef. The restaurant’s meat supplier delivers 150 pounds of pork and 110 pounds of beef each day. Regardless of how it is served on the menu, the restaurant makes about $8.65 per pound for pork barbecue and $10.95 per pound for beef barbecue. The restaurant wants to know how many pounds of each type of barbecue to cook each day in order to maximize profit.
a. Formulate a linear programming model for this problem.
b. Solve this model graphically.