a.) A manufacturer of lawn care equipment has introduced a new product. The anticipated demand is normally distributed with a mean of = 100 and a standard deviation of = 50. Each unit costs $75 to manufacture and the introductory price is to be $125 to achieve this level of sales. Any unsold units at the end of the season are unlikely to be very valuable and will be disposed of in a fire sale for $25 each. It costs $10 to hold a unit in inventory for the entire season. What is the optimal cycle service level? How many units should be manufactured for sale?

b.) In the previous problem, the manufacturer performs additional market research. Based on this research, they determine that they can increase the price to $150 and are able to reduce the standard deviation of the forecast to = 30. At the same time, they have made an arrangement with an outlet store that will purchase unsold equipment for $60 each. What are the optimal cycle service level and optimal order size, respectively?