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A person is opening a boat business on a newly formed take and needs to decide the number of boats to purchase. Because of economic order quantities the boats are best purchased in lots of ten. Assume that the probability that there is a good fish population is p. Profits are estimated based on how well the lake's fish population develops as follows: What is the expected profit if the person chooses to purchase 10 boats? What about 20 boats? What about 30 boats? Draw the profit lines obtained from Question 1 that show how profits change over the value of p. For what range of probability that there's a good fish population, will it be decided to buy 10 boats? What about 20 boats, and 30 boats? Please provide calculation and explanation.

Explanation / Answer

(1)

Expected profit if person chooses
1) 10 boats
Profit = p*1000 + (1-p)*900

2) 20 boats
Profit = p*2500 + (1-p)*500

3) 30 boats
Profit = p*3000 + (1-p)*0

(2)

For different values of p below table shows different values of profits

Probability of Good population p 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Probability of Poor Population 1-p 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 Expected Profit 10 Boats 910 920 930 940 950 960 970 980 990 20 Boats 700 900 1100 1300 1500 1700 1900 2100 2300 30 Boats 300 600 900 1200 1500 1800 2100 2400 2700

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