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

Quizplus · Accepted Answer

The expected payoff for purchasing three dozen T-shirts can be calculated as follows:

Expected payoff = (0.3 x 180) + (0.4 x 120) + (0.2 x 60) + (0.1 x (-20))
= 54 + 48 + 12 - 2
= 112

Therefore, the expected payoff for purchasing three dozen T-shirts is $112.

To determine the best choice, we can calculate the expected payoffs for purchasing each possible quantity of T-shirts and select the one with the highest expected payoff.

Expected payoff for purchasing one dozen T-shirts: 
= (0.3 x 60) + (0.4 x 30) + (0.2 x 0) + (0.1 x (-40))
= 18 + 12 - 4
= 26

Expected payoff for purchasing two dozen T-shirts: 
= (0.3 x 120) + (0.4 x 80) + (0.2 x 40) + (0.1 x (-10))
= 36 + 32 + 8 - 1
= 75

Expected payoff for purchasing three dozen T-shirts: 
= (0.3 x 180) + (0.4 x 120) + (0.2 x 60) + (0.1 x (-20))
= 54 + 48 + 12 - 2
= 112

Expected payoff for purchasing four dozen T-shirts: 
= (0.3 x 240) + (0.4 x 160) + (0.2 x 80) + (0.1 x 0)
= 72 + 64 + 16
= 152

Therefore, the best choice is to purchase four dozen T-shirts, as it has the highest expected payoff of $152.

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