A store selling Christmas trees needs to order 3 months in advance on the number

Question

A store selling Christmas trees needs to order 3 months in advance on the number of trees to stock. Due to time constraint, reordering is not possible. Each tree costs $40 and will be sold for $100. After Christmas Day, trees will be sold by a discount price for $50 (assuming all leftovers can be sold). The historical data shows the demand is uniformly distributed between 20 and 40 trees. Suppose that the storeowner decides to order 30 trees and uses simulation to estimate the expected profit. Assume that 5 replications have been made with demands as follows: 27, 31, 36, 25, and 29.

(a) Estimate the profit for each replication.

(b) Use the above data to estimate the expected total profit with a confidence interval (let =0.1)

Explanation / Answer

Demand follows uniform distribution = 1/40-20 = 1/20

cumulative distribution of demand = (x-a)/(b-a) = x-20/20

estimate the profit for each replication is calculated in the given table.

b) Use the above data to estimate the expected total profit with a confidence interval (let =0.1)

the expected total profit with a confidence interval (let =0.1) is (1228.75,1318.75)

demand tree cost Additional units Selling price Profit on first 20 units Probability of selling over 20 units Estimated profit Probability of not selling Estimated profit (if not sold) Estimated profit for each replication 27 40 7 100 1200 0.65 273 0.35 24.5 1348.75 31 40 11 100 1200 0.45 297 0.55 60.5 1378.75 36 40 16 100 1200 0.2 192 0.8 128 1360 25 40 5 100 1200 0.75 225 0.25 12.5 1318.75 29 40 9 100 1200 0.55 297 0.45 40.5 1368.75B)

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