As the manager of a 90-unit motel you know that all units are occupied when you charge $120 a day per unit. Each occupied room costs $68 for service and maintenance a day. You have also observed that for every 2x dollars increase in the daily rate above $120, there are 3x units vacant. Determine the daily price that you should charge in order to maximize profit. Calculate the number of occupied units. Assuming that fixed cost is $704 calculate optimal profit.