Shady Tree, a manufacturer of lawn care equipment, has introduced a new product. Each unit costs $150 to manufacture. The product will be sold for a price of $200. At this price the expected demand, which is assumed to be normally distributed, will have a mean, mu, equal to 100 and a standard deviation of demand, sigma, equal to 40. Any unsold units at the end of the season will have to be discounted to a price of $50. It costs Shady Tree $20 to hold one of these units in its inventory for the full season.
1. How many units should Shady Tree manufacture for sale?
2. What profit could they expect from their decision?
3. On average, how many customers for this product will Shady Tree expect to have to turn away because of stocking out?