Mugs Direct provides customized coffee mugs and other items to corporations for promotional purposes. For the 4th of July, its two largest clients usually order stars and stripes themed mugs with their company

logo. The demand forecast for each client is independent and normally distributed, with parameters given in the following table.

Client A: mean = 700; standard deviation: 300

Client B: mean = 1100; standard deviation: 450

Currently, Mugs Direct sources their mugs from an offshore supplier who performs the customization for each mug order and ships to Mugs Direct ahead of the selling season. Each mug costs $4 and Mugs Direct sells them to their clients for $15. Because of the customization, mugs unsold to either client are essentially worthless and are donated to charity for free. How many mugs should Mugs Direct order from the offshore supplier for each client, and what is their expected profit for this policy? How many mugs do they expect to donate to charity? Mugs Direct is considering contracting with a local print-shop to customize the mugs after clients place their orders. Given the local print-shop's quick turn-around time, this would allow Mugs Direct to order blank (un-customized) mugs from the offshore supplier and customize only those mugs that are ordered by the client. Leftover blank mugs can then be sold at a salvage value of $2/unit. The offshore supplier charges $3 per blank mug, and the local print-shop charges Mugs Direct $1.50 to customize each mug they sell to a client, while Mugs direct maintains the same price of $15 to their clients. With this ability to postpone customization, how many blank mugs should Mugs Direct order from the offshore supplier, how many do they expect to customize, and what is their expected profit? Do you recommend that Mugs Direct postpones customization by contracting with the local print-shop? How would your recommendation change if the clients' orders were positively correlated?