CustomT Corporation is a web-based custom T-shirt retailer. In preparation for Halloween, the company needs to decide how many of a specific Frightful T-shirt to order in advance from its supplier, which is based in China. From past experience, CustomT estimates that demand for the Frightful T-shirt will be between 2,400 and 3,000 and may be modeled as normally distributed, with mean 2700 and std. dev. 100. Each Frightful T-shirt, which can be sold at a price of $20.00, costs CustomT $6.00 to make, plus an additional variable overhead of about $3.00. CustomT also incurs a cost of $2.00 per shirt to transport it from the supplier in China. Any remaining Frightful T-shirts unsold after Halloween are scrapped, and CustomT receives $5.00 for each.

SHOW ALL WORK. ANSWER ALL PARTS.

A. Newsvendor Quantity: How many Frightful T-shirts should CustomT stock to maximize expected profit?

B. Expected Profit: If CustomT buys 2800 Frightful T-shirts, calculate the resulting expected profit.

C. Probability: If CustomT buys 2800 Frightful T-shirts, what is the chance that its profit will exceed $24,000? [Note: This question relates to profit, not expected profit.]

D. In-stock Probability: Suppose CustomT uses in-stock probability to pick its Frightful T-shirt order quantity for the supplier in China. Which of the following statements is TRUE, if CustomT increases its in-stock probability from 80% to 85%? Explain your choice.

A. Expected profit decreases. B. Order quantity decreases.

C. Order quantity remains unchanged. D. Expected profit increases.