A manufacture has been selling $1550$ television sets a week at $$480$ each. A market survey indicates that for each $$17$ rebate offered to a buyer, the number of sets sold will increase by $170$ per week.

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

$p(x)=$

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

c$)$ If the weekly cost function is $124000+160x,$ how should it set the size of the rebate to maximize its profit?

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