A manufacturer of lawn care equipment has introduced a new product. The anticipated demand is normally distributed with a mean of $\backslash$mu $=100$ and a standard deviation of $\backslash$sigma $=50.$ 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. How many units should be manufactured for sale?