A manufacture has been selling 1050 television sets a week at 390 dollars each. A market survey indicates that for each 13 -dollar rebate offered to a buyer, the number of sets sold will increase by 130 per week.
a) Find the demand function , where is the number of the television sets sold per week, assuming that is linear.
b) How large of a 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?