A company manufacturing laundry sinks has fixed costs of $100 per day but has total costs of $2,500 per day when producing 15 sinks. The company has a daily demand function of q=360p, where q is the number if laundry sinks demanded and p is the price of a laundry sink.

(a) If we assume that the total cost per day is linearly related to the amount of sinks produced in a day, derive the total cost function of the company?

(b) Find a function for the average cost of this company.

(c) If production increases continuously, what is likely to be the average cost per sink?

(d) How many laundry sinks will the company need to produce in order to maximize its profits?

(e) What is the maximum profit?