A manufacture has been selling 1900 television sets a week at $510 each. A market survey indicates that for each $23 rebate offered to a buyer, the number of sets sold will increase by 230 per week....

A manufacture has been selling 1900 television sets a week at $510 each. A market survey indicates that for each $23 rebate offered to a buyer, the number of sets sold will increase by 230 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 161500+170x how should it set the size of the rebate to maximize its profit?