Department Store Problem

As a buyer for a large department store, you must decide how
many of a new style of coat to order. Because of rapid changes
itn fashion, you do not want to order too many coats, but if you
order too few you will lose profits for the department. Each
coat purchased costs € 100 and sells for €200. Any coats not
sold at the end of the season are sold below cost at €50.
Demand is uncertain but previous experience indicates that it
may be high (2,000coats) with a probability of .4, moderate
( 1,000 coats) with a probability of .5 or low (500 coats) with a
probability of.1. Assume that there are only three possible
purchase order levels of 2,000, 1,000 and 500 coats.

(i) Write down the payoff table .
(ii) Calculate the expecled profit for each purchase order
level and decide how many coats should be ordered to
maximise expected profit.
(iii) From past experience it is knlwn that when the demand
is low, a recession occurs 80% of the time and there is
prosperity 20% of the time. On the other hand when
demand is moderate, a recession occurs 60% of the time
and there is prosperity 40% of the time. When demand is
high, a recession occurs only 10% of the time and 90% of
the time there is prosperity. Assuming the economic
forecast is for prosperity. revise the probabilities of the
demand being low, moderate, and high, and hence find
which policy should be pursued in order to maximise the
expected profit.