A designer is planning orders for its annual limited-edition ornament. Demand has been forecast to be normally distributed, with a mean of 20,000 and a standard deviation of 8,000. Each ornament costs $30 and is sold for $95. All unsold ornaments are destroyed at the end of the season, to ensure the value of the limited edition.
a. How many ornaments should the designer order? What is the expected profit?
b. The manufacturer has offered to discount the price to $28 per ornament if at least 25,000 are ordered. How should the designer respond?