The national sales manager for "I colored this" (ICT) T-shirts, provides all salespersons with the opportunity loss table showing the potential lost profit for each purchase decision or act from 1 to 4 dozen T-shirts. The probability of demand for each state of nature is also shown. What is the expected opportunity loss of purchasing 3 dozen T-shirts?
A) 84
B) 108
C) 156
D) 204

Question

The national sales manager for "I colored this" (ICT) T-shirts, provides all salespersons with the opportunity loss table showing the potential lost profit for each purchase decision or act from 1 to 4 dozen T-shirts. The probability of demand for each state of nature is also shown.  What is the expected opportunity loss of purchasing 3 dozen T-shirts?
A) 84 
B) 108 
C) 156 
D) 204

Quizplus · Accepted Answer

To find the expected opportunity loss of purchasing 3 dozen T-shirts, we need to multiply each potential lost profit by its corresponding probability of demand, and then sum the results.

Potential lost profits for purchasing 3 dozen T-shirts: 
- $36 if demand is 1 dozen 
- $24 if demand is 2 dozen 
- $12 if demand is 3 dozen 
- $0 if demand is 4 dozen

Multiplying each potential lost profit by its corresponding probability of demand: 
- $36 x 0.3 = $10.80 
- $24 x 0.5 = $12.00 
- $12 x 0.2 = $2.40 
- $0 x 0 = $0

Summing the results: 
$10.80 + $12.00 + $2.40 + $0 = $25.20

Therefore, the expected opportunity loss of purchasing 3 dozen T-shirts is $25.20, which is closest to option B ($108).

The best choice(s) would be to purchase 4 dozen T-shirts because it has the lowest expected opportunity loss of $8.80.

The National Sales Manager for "I Colored This" (ICT) T-Shirts