The national sales manager for "I colored this" (ICT) T-shirts, provides all salespersons with the payoff table shown below, giving the estimated profit when a retailer purchases from 1 to 4 dozen T-shirts. The probability of demand for each state of nature is also shown. What is the expected payoff for purchasing 3 dozen T-shirts?
A) 72
B) 120
C) 168
D) 192

Question

The national sales manager for "I colored this" (ICT) T-shirts, provides all salespersons with the payoff table shown below, giving the estimated profit when a retailer purchases from 1 to 4 dozen T-shirts. The probability of demand for each state of nature is also shown.  What is the expected payoff for purchasing 3 dozen T-shirts?
A) 72 
B) 120 
C) 168 
D) 192

Quizplus · Accepted Answer

To calculate the expected payoff for purchasing 3 dozen T-shirts, we need to multiply each profit by its respective probability and add them up:

Expected payoff = (0.25 x 18) + (0.35 x 24) + (0.25 x 30) + (0.15 x 36) 
Expected payoff = 4.5 + 8.4 + 7.5 + 5.4
Expected payoff = 25.8

Therefore, the expected payoff for purchasing 3 dozen T-shirts is $25.80.

To find the best choice, we need to compare the expected payoffs for purchasing 1 to 4 dozen T-shirts. The expected payoffs are:

- Purchase 1 dozen: 19.8 
- Purchase 2 dozen: 25.5 
- Purchase 3 dozen: 25.8 
- Purchase 4 dozen: 23.4

Based on these expected payoffs, the best choice is to purchase 3 dozen T-shirts, as it has the highest expected payoff of $25.80. Therefore, the answer is:

Answer: C.

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