An automobile manufacturer finds that 80,000 cars can be sold if each is priced at $12,000. However, the number sold increases by 24 for every $1 decrease in the price. The manufacturer has fixed costs of $45,000,000; in addition, it costs $5,500 to produce each car. How should the cars be priced to maximize profits? I can do this by trial and error but I would like to know how to set up and do this problem the right way. Thanks.