A fashion retailer in Santa Barbara, California, presents a new designer dress at one of the "by invitation only" fashion shows. After the show, the dress will be sold at the company's boutique store for $10,000 apiece. Demand at the boutique is limited due to the short time the dress remains fashionable and is estimated to be normal with mean 70 and standard deviation 40. There were only 100 dresses produced to maintain exclusivity and high price. It is the company's policy that all unsold merchandise is destroyed.
a. How many dresses remain unsold on average at the end of the season?
b. What is the retailer's expected revenue?
c. Fashion companies often sell a portion of new merchandise at exhibitions for a discount while the product is still "fresh" in the minds of the viewers. The company decides to increase revenues by selling a certain number of dresses at a greatly discounted price of $6,000 during the show. Later, remaining dresses will be available at the boutique store for a normal price of $10,000. Typically, all dresses offered at the show get sold, which, of course, decreases demand at the store: it is now normal with mean 40 and standard deviation 25. How many dresses should be sold at the show?
d. Given your decision in part c, what is expected revenue?
e. Given your decision in part c, how many dresses are expected to remain unsold?