Arrowmark Vending has the contract to supply pizza at all ho

Arrowmark Vending has the contract to supply pizza at all home football games for a university in the Big 12 athletic 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 4,000 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 / 0.10

300 / 0.15

400 / 0.15

500 / 0.20

600 / 0.20

700 / 0.10

800 / 0.05

900 / 0.05

Pepperoni and Cheese Demand / Probability

300 / 0.10

400 / 0.20

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 pizza.?

3. Prepare a short report that provides Tom with the information regarding how many of each type of pizza he should produce if he wants to achieve the highest expected profit from pizza sales at the game.

Solution

The following table shows the detailed combination and profits

Assumptions: As per demand pizzas were produced and profits calculated

The table shows profit is more for plain cheese demand.

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If Tom has to get the highest profit 600 plain cheese and 600 pepperoni to be produced.