The Beta Upsilon Sigma honorary business fraternity at Tech wants to open a food booth at the football stadium for the upcoming season as a project to raise money to tutor students in management science courses. There will be six home games in the season and the Tech athletic department charges a vending fee of $1,000 per game to rent a booth. The fraternity plans to sell cheese pizza slices for $4 and hot dogs for $3. They will purchase 16-inch pizzas (each with 8 slices) from a local restaurant for $10 that will be delivered twice per game, an hour before kickoff and after the first quarter. They will make the hot dogs (costing $0.65 each) at a member's house, wrap them in foil, and deliver them at the same time as the pizzas; however, they only have enough time and kitchen capacity at the member's house to make at most 1,000 hot dogs. They have a budget of $1,000 per game to purchase the food. They expect each delivery to be sold by the time the next delivery arrives, and all items will be sold by the end of the game. They will need to purchase a warming oven for $2,600 to store the pizza and hot dogs waiting to be sold. The warming oven has 16 shelves, each with a storage area of 1,728 in2. Pizza boxes and hotdogs cannot be stacked on top of each other on a shelf. A pizza box takes up 324 in2 of space and a hot dog 16 in2. After talking with other vendors the fraternity believes they will sell at least 20% more pizza slices than hot dogs. The fraternity wants to determine how many pizzas to order and hot dogs to make and the profit they will earn.

a. Formulate a linear programming model for this problem.

b. Solve this problem using graphical analysis.