The owners of Sweet-Tooth Bakery have determined thatthey need to expand their facility in order to meet their increaseddemand for baked goods. Th e decision is whether to expand nowwith a large facility or expand small with the possibility of havingto expand again in fi ve years.Th e owners have estimated the following chances for demand:• Th e likelihood of demand being high is 0.70.• Th e likelihood of demand being low is 0.30.Profi ts for each alternative have been estimated as follows:• Large expansion has an estimated profi tability of either$80,000 or $50,000, depending on whether demand turnsout to be high or low.• Small expansion has a profi tability of $40,000, assumingdemand is low.• Small expansion with an occurrence of high demand wouldrequire considering whether to expand further. If the bakeryexpands at this point, the profi tability is to be $50,000.(a) Draw a decision tree showing the decisions, chanceevents, and their probabilities, as well as the profi tabilityof outcomes.(b) Solve the decision tree and decide what the bakery shoulddo.
The owners of Sweet-Tooth Bakery have determined that
they need to expand their facility in order to meet their increased
demand for baked goods. Th e decision is whether to expand now
with a large facility or expand small with the possibility of having
to expand again in fi ve years.
Th e owners have estimated the following chances for demand:
• Th e likelihood of demand being high is 0.70.
• Th e likelihood of demand being low is 0.30.
Profi ts for each alternative have been estimated as follows:
• Large expansion has an estimated profi tability of either
$80,000 or $50,000, depending on whether demand turns
out to be high or low.
• Small expansion has a profi tability of $40,000, assuming
demand is low.
• Small expansion with an occurrence of high demand would
require considering whether to expand further. If the bakery
expands at this point, the profi tability is to be $50,000.
(a) Draw a decision tree showing the decisions, chance
events, and their probabilities, as well as the profi tability
of outcomes.
(b) Solve the decision tree and decide what the bakery should
do.
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