Question

The following payoff table provides profits based on various possible decision alternatives and various levels of demand at Amber Gardner's software firm:

		Demand Level
		0.70	0.30
		Low	High
Alternative	A	$12,500	$30,000
	B	$7,500	$41,000
	C	($2,000)	$50,000
*Profits in $ thousands

1. Using Excel, create an X,Y plot the expected-value lines for the three alternatives on a graph. Label the graph completely and clearly. (5 pts)
2. Is there any alternative that would never be appropriate in terms of maximizing expected profit? Explain on the basis of your graph in part a. (5 pts)
3. Over what range of P(High Demand) would alternative A be the best choice if the goal is to maximize expected profit? Show work. (5 pts)
4. Over what range of P(High Demand) would alternative C be the best choice if the goal is to maximize expected profit? Show work. (5 pts)
5. Compute the expected values for each alternatives if the probability of high demand level as 0.30. Show work. Which of the 3 alternatives is best under this probability? (5 pts)
6. Using the probability of low demand as 0.70 (therefore probability of high demand = 0.30), compute the expected payoffs of each of the alternatives. Show work. Using the expected payoff criterion, which of the alternatives will you recommend? (5 pts)
7. Using the probability of low demand as 0.70 (therefore probability of high demand = 0.30), compute the EVPI. Show work. Explain the significance of this number (i.e. what does it mean?). (10 pts)

Answer 1

a.

b. There is no alternative that would never be appropriate

c.

Let, required probability of High demand is x for alternative A would be best choice

So, x*12500+(1-x)*30000 = x*7500+(1-x)*41000

or, 5000x= 11000-11000x
or, x = 11000/16000 = 0.6875

So for probability range between 0.6875 and 1 of High demand Alternative A would remain best choice

d.

Let, required probability of High demand is x for alternative C would be best choice

So, x*(-2000)+(1-x)*50000 = x*7500+(1-x)*41000

or, 9500x= 9000-9000x
or, x = 9000/18500 = 0.486486486

So for probability range between 0 and 0.486486486 of High demand Alternative C would remain best choice

e.

Expected payoff for Alternative A = 0.7*12500+0.3*30000 = 17750

Expected payoff for Alternative B = 0.7*7500+0.3*41000 = 17550

Expected payoff for Alternative C = 0.7*(-2000)+0.3*50000 = 13600

Using expected payoff criterion recommended alternative is alternative A as it has highest expected payoff

f.Expected payoff for Alternative A = 0.7*12500+0.3*30000 = 17750

Expected payoff for Alternative B = 0.7*7500+0.3*41000 = 17550

Expected payoff for Alternative C = 0.7*(-2000)+0.3*50000 = 13600

Using expected payoff criterion recommended alternative is alternative A as it has highest expected payoff

g.

EVPI = expected payoff with perfect information - expected payoff without perfect information

= 0.7*12500+0.3*50000-17750

= 6000