A manufacturer has been selling 1000 television sets a week at$500each. A market survey indicates that for each $10 rebate offered to the buyer, the number of sets sold will increase by100per week. Round your answers to the nearest dollar.

(a) Find the demand function (price as a function of units sold).

p(x) =

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

$

(c) If the company experiences a cost ofC(x) =62,000+130x, how should the manufacturer set the size of the rebate in order to maximize its profit?

$