A manufacture has been selling 1200 television sets a week at $480 each. A market survey indicates that for each $13 rebate offered to a buyer, the number of sets sold will increase by 130 per week.

a) Find the function representing the demand $p(x)$, where $x$ is the number of the television sets sold per week and $p(x)$ is the corresponding price.
$p(x)=$

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

c) If the weekly cost function is $96000 + 160 x$, how should it set the size of the rebate to maximize its profit? dollars