A manufacture has been selling 1100 television sets a week at $ 360 each. A market survey indicates that for each $ 12 rebate offered to a buyer, the number of sets sold will increase by 120 per week.
(a) Find the price function p(x) , where x is the number of the television sets sold per week.
(b)How large of a rebate should the company offer to a buyer, in order to maximize its revenue? Hint: Solve for the number of TVs, x, that will maximize revenue. Then, find the rebate associated with this number of TVs.
(c) If the weekly cost function is 66000+120x, how should it set the size of the rebate to maximize its profit?