A manufacture has been selling 1300 television sets a week at $510 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)\displaystyle {p}{\left({x}\right)}, where x\displaystyle {x} is the number of the television sets sold per week.
p(x)=\displaystyle {p}{\left({x}\right)}=  

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

c) If the weekly cost function is 110500+170x\displaystyle {110500}+{170}{x}, how should it set the size of the rebate to maximize its profit?
$  

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