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Problem-02: A survey conducted over the last 20 years in Hamburg., Germany indicated that in 8 of them the winter was mild, in 7 of them it was cold, and in the remaining 5 it was very cold. A company sells 1,000 heavy coats in a mild year., 1,300 in a year, and 2,000 in a very cold year.
                   Find the yearly expected profit of the company if a coat costs 85 deutsche marks (DM) and is sold to stores for 123 DM.

Solution:
According to the question,
* States of nature: (i) Mild, (ii) Cold, (iii) Very cold
* Alternative courses of Action: Selling of heavy coats.
Probabilities of states of natures:
(i) Mild = 8/20 = 0.4
(ii) Cold = 7/20 = 0.35
(iii) Very cold = 5/20 = 0.25

You can also read: Decision Analysis » Problem-01 Solution | Operations Research

Table for the calculation of Expected Value

Probabilities 0.4 0.35 0.25 1
States of Nature Mild Cold Very cold Expected Value
Courses of Action
Selling of heavy coats 1,000 1,300 2,000 1,355

Expected profit of coat = 123 - 85 = 38
∴ Expected total profit = 38 × 1,355 = 51,490

N.B:

How to calculate Expected value:
EV = (1,000 × 0.4) + (1,300 × 0.35) + (2,000 × 0.25) = 1,355

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