A retailer of Chinese lanterns must decide how many lanterns to order for the 2024 Chinese New year festival. The retailer buys the lanterns from a supplier at USD 15 each and sells them for USD 40. There is only one opportunity to buy lanterns from the supplier. Lanterns left over at the end of the Chinese New Year selling season are sold at a discounted price of USD 8 each. The retailer assumes that the demand is approximately normally distributed with a mean of 600 lanterns and a standard deviation of 200 lanterns:

a. How many lanterns should the retailer buy from the supplier?

b. How would the retailers order quantity change if the demand was approximately normal, with an average of 600 and a standard deviation of 100 lanterns? Explain this change (or, if there is no change).

c. How would the order quantity change if the demand was uniformly distributed between 400 and 800 lanterns?

d. Now assume that the retailer can buy, on the spot market, as many additional lanterns as needed from its competitor at USD 30 each during the Chinese New year season. How many lanterns should the retailer order from the lantern supplier at the start of the Chinese New Year season to meet the normally distributed demand of an average of 600 and a standard deviation of 200?