A manufacturer has been selling 1,000 flat-screen TVs a week at $500 each. A market survey indicates that for each $10 rebate offered to the buyer, the number of TVs sold will increase by 100 per week. (a) Find the demand function (price p as a function of units sold x). p(x) = (b) How large a rebate (in dollars) should the company offer the buyer in order to maximize its revenue? $ (c) If its weekly cost function is C(x) = 64,000 + 120x, how should the manufacturer set the size of the rebate (in dollars) in order to maximize its profit? $