Question

A tire manufacturer is considering various locations in a particular geographical area for a franchise retail store. After careful consideration, the company represents the problem with the following decision table. The numbers in the table are estimated annual sales.

	States of Nature
	Economic growth	Economic stagnation
Locate in Beachtown	$350,000	$250,000
Locate in Sun City	$400,000	$200,000
Locate in Oldville	$150,000	$275,000

a. Perform Sensitivity Analysis for the tire manufacturer by plotting the Expected Value for each alternative against the Probability of Economic Growth. (Only one graph should be created)

b. Write an interpretation of your graph

Answer 1

Let p= probability of Economic growth. Then 1-p is the probability of Economic stagnation

the expected value of each of the alternatives is

• Locate in Beachtown

• Locate in Sun City

• Locate in Oldville

The following table in excel can be created

get these values

plot a graph using, insert--->scatter-->lines

get this graph and format as needed

We can identify the regions in the graph in which a particular alternative is the best

In the left most region, to Locate in Oldville is the best decision.

To find the exact probability, we will equate the EV for green line with the blue line

This means for the probability of Economic growth less than 0.11, it makes sense to locate at Oldville.

In the right most region, it locate in suncity gives the highest EV

Equating the EV of red and blue lines we get

This means for the probability of Economic growth greater than 0.5, it makes sense to locate at Suncity.

For the middle portion, when the probability of economic growth is between 0.11 to 0.5, locating at Beachtown gives the highest EV.

b) When the probability of Economic growth less than 0.11, it makes sense to locate at Oldville. When the probability of economic growth is between 0.11 to 0.5, locating at Beachtown gives the highest EV. For the probability of Economic growth greater than 0.5, it makes sense to locate at Suncity.