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.