solved numerical of decision theory (decision making under risk). from aktu question paper

1. Decision Theory Numerical

2. Suppose a grocer is faced with the problem of how many cases of milk
to stock to meet tomorrow’s demand. All the cases of milk left at the
end of the day are worthless. Each case of milk is sold for Rs.8 and is
purchased for Rs.5. Hence, each case sold brings a profit of Rs.3 but if it
is not sold at the end of the day, then it must be discarded resulting in
as loss of Rs.5. The historical record of the number of cases of milk
demanded is as follows. What should be the optimal decision of the
grocer concerning the number of cases of milk to stock? Assuming that
the grocer has a perfect knowledge, then what would be his expected
profit? (2005)

3. Number of cases of
milk demanded
Number of times
demanded
Probability
0-12 0 0.00
13 5 0.05
14 10 0.10
15 20 0.20
16 30 0.30
17 25 0.25
18 10 0.10
Over 18 0 0.00
Total 100 1.00

4. Course of Action
13 14 15 16 17 18 P
State of Nature
13 39 34 29 24 19 14 0.05
14 39 42 37 32 27 22 0.1
15 39 42 45 40 35 30 0.2
16 39 42 45 48 43 38 0.3
17 39 42 45 48 51 46 0.25
18 39 42 45 48 51 54 0.1
EMV 39 41.6 43.4 43.6 41.4 37.2
EV with PI 47.7