Target is trying to decide how many Peyton Manning jerseys to order for the upcoming football season. The jerseys sell for $50, and Target believes that the demand at this price is normally...

Target is trying to decide how many Peyton Manning jerseys to order for the upcoming football season. The jerseys sell for $50, and Target believes that the demand at this price is normally distributed with a most likely value of 200 and a 95% chance of being between 120 and 280. If Target orders 200 jerseys, its cost is $27.00 per jersey.


Every increment of 50 jerseys reduces the unit cost of a jersey by $1.35. For example, if the order quantity is from 250 jerseys to 299 jerseys, the unit cost for each is $25.65. After the Super Bowl, the jerseys will be marked down to a sale price of $20. Historically, demand for sale-price items has followed a normal distribution with mean equal to half the actual full price demand and standard deviation equal to 20% of the mean demand at the sale price. How many jerseys (within 10) should Target order to maximize its expected profit? You can assume that any jerseys not sold at the marked-down price have no value.