What is the maximum amount that the league office should be willing to pay for the service of this agency?

Special Event Planning

The National Football League orders Super Bowl t-shirts from manufacturers in September. The shipment will arrive in late December and t-shirts will be sold from January to February of the following year. Each t-shirt is sold for $30 and costs the league office $10. Remaining unsold t-shirts are marked down after the Super Bowl and are sold to discount retailers for $5.

a. Based on historical data, the league office believes that the demand for Super Bowl t-shirts will be normally distributed with mean 4,000,000 and standard deviation 800,000. How many t-shirts should the league office order to maximize the expected profit?

b. Assume that the league office orders 5,000,000 t-shirts. How many t-shirts can the league office expect to sell at full price ($30)?

c. The league office has contacted a marketing agency to explore the possibility of launching a social media campaign to boost Super Bowl t-shirt sales. The league office expects that the agency will be able to change the demand distribution so that it’s normally distributed with mean 5,000,000 and standard deviation 1,500,000. What is the maximum amount that the league office should be willing to pay for the service of this agency?