The H&S Motor Company produces small motors at a production cost of $$30$ per unit. Defective motors can be reworked at a cost of $$12$ each. The company produces $100$ motors per day and averages $88$ percent good quality motors. Based on past experience, $50\%$ of the defective motors can be reworked prior to shipping to customers. These are also considered good motors. A good motor can be sold for $$100$ while a defective motor can be scrapped and sold for $$16.$ Income consists of both the revenue from the sold motors and the scrapped motors.