A manufacture has been selling 1500 television sets a week at 450 each. A market survey indicates that for each 29 rebate offered to a buyer, the number of sets sold will increase by 290 per week.

a) Find the demand function , where is the number of the television sets sold per week.

b) How large rebate should the company offer to a buyer, in order to maximize its revenue?

c) If the weekly cost function is , how should it set the size of the rebate to maximize its profit?