Arrowmark Vending has the contract to supply pizza at all home football games fo

Question

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.

Explanation / Answer

We are provided with the following information:

The fixed cost for making the pizzas is $1000.

The demand distribution is as follows:

1. The expected profit is given as follows

Cheeze pizza

Thus, the expected profit from the sales of cheese pizzas at different level of demand is=

0.10x$900 + 0.15x$1350 + 0.15x$1800 + 0.20x$2250 + 0.20x$2700 + 0.10x$3150 + 0.05x$3600 =$2047.5

Pepporini and cheese pizza

Thus the expected profit from the sales of Pepporini and cheese pizza at different levels of demand is=

0.10x$1200 + 0.20x$1600 + 0.25x$2000 + 0.25x$2400 +0.15x$2800 +0.05x$3200 =$2120

2.For a given level the expected profit can be given as:

A

(1)*(2)

B

(3)*(4)

A+B

Expected Profit

3. From the above table we can tell Tom that if a)he wants to stick at one level of production then he should produce 600units of each pizza as at this level the profit earned is maximum i.e $1140 which after reducing the fixed cost of $1000 fives a net profit of $140. If tom chhoses to produce at any other level then he is expected to make a loss as all other profit values are less than $1000. So, to get the higest expected profit he should produce 600 units of each.

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