Question

Cheryl Druehi Retailers, Inc., must decide whether to build a small or a large facility at a new location in Fairfax. Demand at the location will either be low or high, with probabilities 0.3 and 0.7, respectively. If Cheryl builds a small facility and demand proves to be high, she then has the option of expanding the facility. If a small facility is built and demand proves to be high, and then the retailer expands the facility, the payoff is $280,000. If a small facility is built and demand proves to be high, but Cheryl then decides not to expand the facility, the payoff is $183,000. If a small facility is built and demand proves to be low, then there is no option to expand and the payoff is S210,000. If a large facility is built and demand proves to be low. Cheryl then has the option of stimulating demand through local advertising. If she does not exercise this option, then the payoff is $60,000. If she does exercise the advertising option, then the response to advertising will either be modest or sizable, with probabilities of 0.4 and 0.6, respectively. If the response is modest, the payoff is $50,000. If it is sizable, the payoff is $220.000. Finally, if a large facility is built and demand proves to be high, then no advertising is needed and the payoff is $700,000. a) What should Cheryl do to maximize her expected payoff? Choose the correct decision tree below. Note that all payoffs are in S1,000s. OA OB 210 Q 210 Q low (0.3) low (0.3) expand expand 2 280 2 280 Small high (0.71 large high (0.77 don't expand 192 modest (0.4) 50 don't expand 183 modest (0.4) 50 1 1 advertise sizable 220 advertise salle 220 1061 large low (0.3) Small low (0.3) 3 60 3 60 don't advertise don't advertise high (0.7) high (0.7) 700 700
need help with the first part as well, accidentally clicked on a graph

Answer 1

from the given en data, the decision tree becomes: a) $210k low (0.3) High 12 Expand $280k Small 10:7) Dont expand large 13 advertise $183K modest $ SOK low (6 (0.4) (0:3) sizeable $220k (0.6) dont advertise $60k High $7ook (0.7) =) Correct decision tree is A) Expected value at o Expected value at o E CProbability xpayos? =) -> 152 E12) = Max { 280,1835 = 280 E (smael) = 0.3(210) +07(280) = $259k E16)=0.4(50) +0.6(220) E(3) = Max { 152,60} = Ellarge) = 0-3 (152) +0.7(700) = 1535.6k =) Cheryl should build large facility, if demand proves to be low then advertise to stimulate demand. b) Expected Pay off $ 535600