Green Thumb, a manufacturer of lawn care equipment, has introduced a new product. Each unit costs $$150$ to manufacture, and the introductory price is $$200.$ At this price, the anticipated demand is normally distributed, with a mean of

and a standard deviation of

Any unsold units at the end of the season will be disposed of in a post$-$season 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? What is the expected profit from this policy? On average, how many customers does Green Thumb expect to turn away because of stocking out?