Theory of Expectation :: Problems on Profits, Business : Probability Distribution

Solution

Profit earned = [(No. of pieces Sold) × (Selling Price Per Piece)]     − [(No. of Pieces manufactured) × (Cost per Piece)] = (No. of pieces Sold) × (Rs. 3.00)     − [(No. of Pieces manufactured) × (Rs. 1.00)] Sale realisation on sale of 10 pieces ⇒ 10 × 3.00 = Rs. 30 11 pieces ⇒ 11 × 3.00 = Rs. 33 12 pieces ⇒ 12 × 3.00 = Rs. 36 Cost incurred on the manufacture of 12 pieces ⇒ 12 × 1.00 = Rs. 12.00 Therefore, the Profit earned = Sale Realisation − Cost Incurred Therefore, the profit made by the man when he sells 10 pieces would be Rs. 18 (Rs. 30 − Rs. 12) when he sells 11 pieces would be Rs. 21 (Rs. 33 − Rs. 12) when he sells 12 pieces would be Rs. 24 (Rs. 36 − Rs. 12) In this decision making problem Since the decision with regard to how many pieces should be manufactured is in the hands of the proprietor of the food stall, no. of pieces to be manufactured would form the acts. Since how many pieces would be demanded is something not within the hands or control of the proprietor of the food stall, the no. of pieces demanded would form the states of nature. Each state of nature has a certain probability of occurance. The probabilities for the states are not varying with the acts i.e. the probability for a state of nature is the same whatever may be act that the proprietor of the food stall chooses. Calculations for profits made under various situations No. Manufactured → Demanded ↓ 12 10 18 11 21 12 24 13 24 14 24 15 24 Even in cases where there is demand greater than 12 units he can make a profit of Rs. 24 only since he can sell only 24 units. Calculations for expected profit Manufactured → 12 Demanded ↓ Prob Pr Exp Pr 10 0.07 18.00 1.26 11 0.10 21.00 2.10 12 0.23 24.00 5.52 13 0.38 24.00 9.12 14 0.12 24.00 2.88 15 0.10 24.00 2.40 Total Expected Profit 23.28 Pr. ⇒ Profit and Exp. Pr ⇒ Expected Profit The proprietor of the food stall can expect to make a profit of Rs. 23.28