Gator Sports Inc.(GSI) is a retailer of high-end sporting goods. One of the products GSI sells for which it has an exclusive agreement with the manufacturer is the Wet-Smart wet suit. GSI sells the wet suit for $200 while it pays $100 per suit. If GSI has leftover inventory at the end of the season, it is GSI's experience that they are able to sell that inventory for $40/unit. Tim O'Neill, who is the purchasing manager, is getting ready to place their order for the season. Tim believes that the demand for Wet-Smart during the selling season follows a normal distribution with a mean of 100 and a standard deviation of 20.

1. How many wet suits should Tim order to maximize expected profits?
2. Bob is Tim's boss and he thinks the company should adopt a service level of 0.85 for these wet suits. His reason is that any customer who is not able to buy the Wet-Smart wet suit because GSI is out-of-stock,would take his/her business elsewhere and GSI would lose significant revenues and therefore profits.

a. What is the optimal order size associated with the 0.85 service level?

b. What is the goodwill cost implied by the 0.85 service level?