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You are a newsvendor selling San Pedro Times every morning. Before you get to work, you go to the printer and buy the day’s paper for $0.35 a copy. You sell a copy of San Pedro Times for $0.75. However, any unsold papers can be returned to the printer for a $0.15 refund per copy. If the demand for the San Pedro Times is normally distributed with a mean of 60 and a standard deviation of 10, how many copies of San Pedro Times should you buy to maximize your expected profit? What is the expected profit in this scenario?

a. 60 copies; $15.00

b. 55 copies; $12.00

c. 65 copies; $20.00

d. 50 copies; $10.00

User Rejaul
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1 Answer

4 votes

Final answer:

The optimal number of copies to purchase is approximately 65, with an expected profit higher than $20.00. This calculation uses the newsvendor model, considering the cost to buy, sell, and refund for unsold papers.

Step-by-step explanation:

To determine the optimal number of copies of the San Pedro Times to purchase, we must consider the cost of buying and selling papers as well as the refunds for unsold copies. We need to calculate the newsvendor's critical ratio, which is the profit from selling one additional copy divided by the profit plus the loss from not selling that copy. The cost to buy a paper is $0.35, the selling price is $0.75, and the refund for unsold papers is $0.15. Hence, the profit from selling a paper is $0.75 - $0.35 = $0.40, and the loss from not selling a paper is $0.35 - $0.15 = $0.20.

The critical ratio (CR) is therefore $0.40 / ($0.40 + $0.20) = 0.6667. To find the optimal order quantity (Q*), we use the inverse standard normal distribution function to find the z-score that corresponds to a CR of 0.6667. Given the demand with a mean (mu) of 60 and standard deviation (sigma) of 10, we can calculate Q* using the formula Q* = mu + z * sigma. The z-score that corresponds to 0.6667 is approximately 0.43, thus Q* = 60 + 0.43 * 10 ≈ 64.3, which we'll round to 65 copies for practical purposes.

The expected profit is calculated by taking the expected sales minus the costs and adding the refunds for unsold copies. Since we cannot have an exact calculation here, we'll assume an optimal order quantity close to 65 maximizes the expected profit. Neither of the options given corresponds exactly to the calculation, but the closest one is 65 copies with an expected profit that we estimate to be slightly higher than $20.00.

User Deebs
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8.8k points
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