Problem 1 (10 points): Green Thumb, a manufacturer of lawn care equipment, has introduced a new product. Each unit costs $150 to manufacture, and the introductory price is to be $200. a) At this price, the anticipated demand is normally distributed, with a mean of = 100 and a standard deviation of = 40. Any unsold units at the end of the season are unlikely to be valuable and will be disposed of in a fire sale for $50 each. It costs $20 to hold a unit in inventory for the entire season. How many units should Green Thumb manufacture for sale? b) The general manager at Green Thumb decides to conduct extensive market research for its new product. At the end of the market research, the manager estimates demand to be normally distributed, with a mean of = 100 and a standard deviation of = 15. How should Green Thumb alter its production plans as a result of the market research?