Pizza and Plain Cheese

Arrowmark Vending has the contract to supply pizza at all home football games for a university in the Big 12 atheletic conference. It is a constant challenge at each game to determine how many pizzas to have available at the games. Tom Kealey, operations manager for Arrowmark, has determined that his fixed cost of providing pizzas, whether he sells 1 pizza or 4000 pizzas, is $1,000. This cost includes hiring employees to work at the concession booths, hiring extra employees to cook the pizzas the day of the game, delivering them to the game, and advertising during the game. He believes that this cost should be equally allocated between two types of pizzas.

Tom has determined that he will supply only two types of pizzas: plain cheese and pepperoni and cheese combo. His cost to make a plain cheese pizza is $4.50 each, and his cost to make pepperoni and cheese combo is $5.00 each. Both pizzas will sell for $9.00 at the game. Unsold pizzas have no value and are donated to a local shelter for the homeless.

Past experience has shown the following demand distributions for the two types of pizza at home games:

Plain Cheese Demand/Probability
200 / 0.1
300 / 0.15
400 / 0.15
500 / 0.2
600 / 0.2
700 / 0.1
800 / 0.05
900 / 0.05

Pepperoni and Cheese Demand / Probability
300 / 0.1
400 / 0.2
500 / 0.25
600 / 0.25
700 / 0.15
800 / 0.05

1) For each type of pizza, determine the profit (or loss) associated with producing at each possible demand level. For instance, determine the profit if 200 plain cheese pizzas are produced, and 200 are demanded. What is the profit if 200 plain cheese pizzas are produced, but 300 were demanded, and so on.

2) Compute the expected profit associated with each possible production level (assuming Tom will only produce at one of the possible demand levels) for each type of