Demand (units) 10
11
12
13
14
Probability
0.10
0.10
0.25
0.40
0.15
The cost of one phone is Rs. 1300 and the sale price is Rs. 2000. If the phone is not sold, then
the loss per unsold set is Rs. 300. How many mobile phone sets should be stocked to expect
maximum profit?
Answers
Given : The cost of one phone is Rs. 1300 and the sale price is Rs. 2000. If the phone is not sold, then the loss per unsold set is Rs. 300
To Find : How many mobile phone sets should be stocked to expect maximum profit?
Solution:
Demand (units) 10 11 12 13 14
Probability 0.10 0.10 0.25 0.40 0.15
S = in Stocks
D = demand
Conditional Profit = 700 * S if D ≥ S
700 *D - 300* (S - D) = 1000D - 300S if D < S
D Probability Profit as per Stock
10 11 12 13 14
10 0.1 7000 6700 6400 6100 5800
11 0.1 7000 7700 7400 7100 6800
12 0.25 7000 7700 8400 8100 7800
13 0.4 7000 7700 8400 9100 8800
14 0.15 7000 7700 8400 9100 9800
Expected profit by multiplying with corresponding probabilities
Stock = 10
7000 (0.1 + 0.1 + 0.25 + 0.4 + 0.15) = 7000
Stock 11
6700 * 0.1 + 7700 ( 0.1 + 0.25 + 0.4 + 0.15) = 7600
Stock 12
6400 * 0.1 + 7400 * 0.1 + 8400 (0.25 + 0.4 + 0.15) = 8100
Stock 13
6100 * 0.1 + 7100 * 0.1 + 8100* 0.25 + 9100( 0.4 + 0.15) = 8350
Stock 14
5800 * 0.1 + 6800 * 0.1 + 7800* 0.25 + 8800* 0.4 + 9800* 0.15) = 8200
Profit is maximum when Stock = 13
He should stock 13 Mobile to expect maximum profit
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