Cheryl Druehl​ 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 ​$230,000. If a small facility is built and demand proves to be​ high, but Cheryl then decides not to expand the​ facility, the payoff is ​$203,000.   If a small facility is built and demand proves to be​ low, then there is no option to expand and the payoff is ​$250,000. 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 $40,000. 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 ​$25,000. If it is​ sizable, the payoff is ​$210,000. ​Finally, if a large facility is built and demand proves to be​ high, then no advertising is needed and the payoff is ​$300,000. ​ Cheryl should build the _ facility. If demand proves to be low​, then _ to stimulate demand. ​ What is the value of this expected​ payoff?   The expected payoff is

Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter9: Decision Making Under Uncertainty
Section9.4: The Precision Tree Add-in
Problem 9P
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Cheryl Druehl​ 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 ​$230,000. If a small facility is built and demand proves to be​ high, but Cheryl then decides not to expand the​ facility, the payoff is ​$203,000.
 
If a small facility is built and demand proves to be​ low, then there is no option to expand and the payoff is ​$250,000. 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 $40,000. 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 ​$25,000.
If it is​ sizable, the payoff is ​$210,000. ​Finally, if a large facility is built and demand proves to be​ high, then no advertising is needed and the payoff is ​$300,000.
Cheryl should build the _ facility. If demand proves to be low​, then _ to stimulate demand.
What is the value of this expected​ payoff?
 
The expected payoff is
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