Tech Fiber (TF) is a manufacturer of synthetic fibers used in ski jackets and other winter outerwear. TF has patented a new lightweight fiber that is very inexpensive to manufacture but has the warmth and water-repellent properties of very expensive natural fibers. TF has designed a new jacket using this fiber that it wants to bring to the market. The jacket will be sold exclusively through Ski Adventure (SA), a major retailer of winter apparel and sport equipment. Each jacket costs $10 to produce and TF plans to charge a wholesale price of $100 per jacket from the retailer. The retailer plans to sell the jacket for a price of $200. At this price, the manager at SA estimates the demand for the new jacket to be normally distributed with a mean of 1,000 and a standard deviation of 300. SA is unable to salvage anything for unsold jackets.

(a) [1] What is the optimal service level if the ordering decision is made by the manager of SA, i.e. maximizing SA profit only?