Question

Kris is considering taking her poutine food truck to the local wine festival to vend. She is pondering the amount of food to stock. High demand Average demand Low demand Large stock

a) Given the payoff matrix, what is her decision under maximax?

b) Given the payoff matrix, what is her decision under maximin?

c) Given the payoff matrix, what is her decision under equally likely?

d) The probability of high demand is 0.3, medium demand 0.5, and 0.2 for low demand. If she is rational and risk-neutral, which alternative should she select, given the payoffs below?

e) What is the EVPI?

	High demand	Average demand	Low demand
Large Stock	$22,000	$12,000	-$2,000
Medium Stock	$14,000	$10,000	$6,000
Small Stock	$9,000	$8,000	$4,000

***Show your Work***

Answer 1

A.

Under the MaxiMax criteria, the best of the maximum payoffs of all the alternatives will be selected.

Maximum payoff under large stock = $22000

Maximum payoff under medium stock = $14000

Maximum payoff under small stock = $9000

The , best of above payoff is $22000, so large stock alternative will be selected.

B.

Under the MaxiMin criteria, the best of the minimum payoffs of all the alternatives will be selected.

Minimum payoff under large stock = -$2000

Minimum payoff under medium stock =$6000

Minimum payoff under small stock =$4000

The , best of the above payoffs is $6000, so medium stock alternative will be selected.

C.

Under equally likely criteria,

Expected payoff under the large stock = (22000 + 12000 -2000)/3 = $10666.67

Expected payoff under the medium stock = (14000 + 10000+6000)/3 = $10000

Expected payoff under the small stock = (9000+8000+4000)/3 = $7000

The maximum payoff is with the large stock alternative, then large stock alternative is selected.

D.

With the given probabilities,

Expected payoff under the large stock = (.3*22000 + .5*12000 -.2*2000) = $12200

Expected payoff under the medium stock = (.3*14000 + .5*10000+ .2*6000) = $10400

Expected payoff under the small stock = (.3*9000 + .5*8000 + .2*4000) = $7500

The maximum payoff is with the large stock alternative, then large stock alternative is selected.

E.

EVPI = EVWPI - EVWOPI

EVPI = (.3*22000 + .5*12000 + .2*6000) - 12200

EVPI = $1600