# Question

F.J. Brewerton Retailers, Inc., must decide whether to build a small or a large facility at a new location in south Texas. Demand at the location will either be low or high, with probabilities 0.4 and 0.6, respectively. If Brewerton builds a small facility and demand proves to be high, he then has the option of expanding the facility. If a small facility is build and demand proves to be high, and then the retailer expands the facility, the payoff is $270,000. If a small facility is build and demand proves to be high, but Brewerton then decides not to expand the facility, the payoff is $223,000.

If a small facility is build and demand proves to be low, then there is no option to expand and the payoff is $200,000. If a large facility is build and demand proves to be low, Brewerton then has the option of stimulating demand through local advertising. If he does not exercise this option, then the payoff is $40,000. If he does exercise the advertising option, then the response to advertising will either be modest or sizable, with probabilities of 0.3 and 0.7, respectively. If the response is modest, the payoff is $20,000. If it is sizable, the payoff is $220,000. Finally, if a large facility is build and demand proves to be high, then no advertising is needed and the payoff is $800,000.

(a) What should Brewerton do to maximize his expected payoff?

(b) What is the value of this expected payoff?

If a small facility is build and demand proves to be low, then there is no option to expand and the payoff is $200,000. If a large facility is build and demand proves to be low, Brewerton then has the option of stimulating demand through local advertising. If he does not exercise this option, then the payoff is $40,000. If he does exercise the advertising option, then the response to advertising will either be modest or sizable, with probabilities of 0.3 and 0.7, respectively. If the response is modest, the payoff is $20,000. If it is sizable, the payoff is $220,000. Finally, if a large facility is build and demand proves to be high, then no advertising is needed and the payoff is $800,000.

(a) What should Brewerton do to maximize his expected payoff?

(b) What is the value of this expected payoff?

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