# Arrowmk Case Study

585 words - 3 pages

I. Introduction
Arrowmark Vending has the contract to supply pizza at football games for a university. The operations
manager, Tom Kealey, faces the challenge of determining how many pizzas to make available at the games.
We have been provided with demand distributions for pizza based on past experience and know that Tom will
only supply plain cheese and pepperoni and cheese combo pizzas. We also know that there is a fixed cost of
\$1,000 allocated equally between the two types of pizzas, and that the costs to make plain cheese pizza and
pepperoni and cheese pizza are \$4.50 and \$5.00 respectively. Both pizzas sell for \$9.00 and unsold pizzas have
no value. The purpose of this report is to provide Tom with some information regarding how many of each
type of pizza he should produce if he wants to achieve the highest expected profit from pizza ...view middle of the document...

This profit will result regardless of whether more than
200 are demanded. Accordingly, if 400 cheese pizzas are produced and only 200 demanded, there is a potential
loss of \$500.
Using these distributions, we are then able calculate the distribution’s mean, which is the expected
value of the profits at each level of production. The expected profits in this case are the weighted average of
the potential profit values, in which the weights are the probabilities. The expected profits associated with each
type of pizza are provided in the tables below:

200
300
400
500
600
700
800
900
Total

300
400
500
600
700
800
Total

200
\$40
\$60
\$60
\$80
\$80
\$40
\$20
\$20
\$400
300
\$70
\$140
\$175
\$175
\$105
\$35
\$700

Expected Profits at each Production Level
300
400
500
600
700
800
-\$5
-\$50
-\$95
-\$140
-\$185
-230
\$128
\$60
-\$8
-\$75
-\$143
-210
\$128
\$195
\$128
\$60
-\$8
-75
\$170
\$260
\$350
\$260
\$170
80
\$170
\$260
\$350
\$440
\$350
260
\$85
\$130
\$175
\$220
\$265
220
\$43
\$65
\$88
\$110
\$133
155
\$43
\$65
\$88
\$110
\$133
155
\$760
\$985
\$1,075
\$985
\$715
\$355
400
\$20
\$220
\$275
\$275
\$165
\$55
\$1,010

500
-\$30
\$120
\$375
\$375
\$225
\$75
\$1,140

600
-\$80
\$20
\$250
\$475
\$285
\$95
\$1,045

700
-\$130
-\$80
\$125
\$350
\$345
\$115
\$725

900
-275
-277.5
-142.5
-10
170
175
132.5
177.5
\$(50)
800
-\$180
-\$180
\$0
\$225
\$270
\$135
\$270

III. Recommendation
If Kealey wants to achieve the highest expected profit from pizza sales at the game, he should produce
500 cheese pizzas and 500 pepperoni and cheese pizzas. Looking at the tables, we know this is the best option
because we see the highest expected profit of \$1,075 associated with this production level for cheese pizza and
\$1,140 in profit for pepperoni and cheese pizza. This number takes into account the probabilities at each
demand level, so we can be reasonably assured that this is an accurate recommendation.

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