University of Iowa Sports Information (UISI) procures its game-day football magazines from a publishing company at a price of $9.00 per magazine. UISI sells the magazines on the day of the corresponding football game at a retail price of $10.00. To sell these magazines, UISI hires vendors and pays them $0.50 for each program that they sell. For the first game of the season, UISI has determined that demand for the game-day football magazines is normally distributed with a mean of 9000 magazines and a standard deviation of 400 magazines. Any magazines that are not sold on the day of the game are worthless and UISI recycles them.

a. What is UISI's optimal order quantity of game-day football magazines for the first game of the season?

b. Instead of recycling the unsold programs, suppose the publisher offers to buy back any unsold programs for $8.00. Under this scenario, what is UISI's optimal order quantity?