Question

The payoff table in millions of dollars of a company that is considering constructing a facility is given below for three states of nature (Demand). Answer Questions 58 to 61 based on the information given in this table. The numbers in parentheses are probabilities of the states of nature.

Action	Demand
	High (0.2)	Moderate (0.3)	Low (0.5)
Build small	$50	$35	$10
Build medium	$120	$70	$0
Build large	$200	100	-$60

What is the best course of action to take?

Group of answer choices

a. Build small

b. Build medium

c. Build large

d. Can not be determined.

What is the highest expected monetary payoff?

Group of answer choices

a. $40

b. $45

c. $50

d. $25.5

What is the expected monetary value under certainty?

Group of answer choices

a. $75

b. 45

c. $66

d. None of the above

Answer 1

Q1) We first obtain the expected payoffs under each of the 3 decisions here as:
E(build small) = 50*0.2 + 35*0.3 + 10*0.5 = 25.5
E(Build medium) = 120*0.2 + 70*0.3 + 0*0.5 = 45
E(Build large) = 200*0.2 + 100*0.3 - 60*0.5 = 40

As the largest expected payoff is under build medium, therefore build medium is the correct answer here.

Q2) From the previous question, we see that largest expected payoff was for Build mediuam which was equal to 45. Therefore b) $45 is the correct answer here.

Q3) Expected value under certainty is computed by taking the maximum payoffs under each of the sitautions with their respective probabilities. Therefore it is computed here as:

= 0.2*200 + 0.3*100 + 0.5*10

= 40 + 30 + 5

= 75

Therefore a) $75 is the expected payoff here.