A manufacturer has been selling 1000 television sets a week at $450 each.

A manufacturer has been selling 1000 television sets a week at $450 each. A market survey indicates that for each $10 worth of rebate offered to buyers, the number of sets sold will increase by 100 per week. (a) Find the demand function. (b) How large a rebate should the company offer buyers in order to maximize its revenue? (c) If its weekly cost function is C(x) = 68000 + 150x, how should the manufacturer set the size of the rebate in order to maximize its prot?