Question

Deborah Hollwager, a concessionaire for the Amway Center in Orlando, has developed a table of conditional values for the various alternatives (stocking decision) and states of nature (size of crowd): Alternatives Large Inventory Average Inventory Small Inventory States of Nature (size of crowd) Large Average Small $24,000 $10,000 - $3,000 $12,000 $15,000 $6,000 $9,000 $6,000 $5,000 Probabilities associated with the states of nature are 0.30 for a large crowd, 0.55 for an average crowd, and 0.15 for a small crowd. a) The alternative that provides Deborah the greatest expected monetary value (EMV) is

Answer 1

Solution:

(a) The Expected Monetary Value (EMV) is calculated using the below formula:

EMV = Sum of (Probability of states of nature x Return on states of nature)

Large Inventory:

​​​​​​​EMV = (0.30 x $24,000) + (0.55 x $10,000) - (0.15 x $3,000)

EMV = $7,200 + $5,500 - $450

EMV = $12,250

Average Inventory:

​​​​​​​EMV = (0.30 x $12,000) + (0.55 x $15,000) + (0.15 x $6,000)

EMV = $3,600 + $8,250 + $900

EMV = $12,750 (Greatest)

Small Inventory:

​​​​​​​EMV = (0.30 x $9,000) + (0.55 x $6,000) + (0.15 x $5,000)

EMV = $2,700 + $3,300 + $750

EMV = $6,750

Answer: Based on the above calculations, the alternative that provides Deborah the greatest expected monetary value (EMV) is Average Inventory.

The EMV of this decision is $12750