A manufacture has been selling 1250 television sets a week at $390 each. A market survey indicates that for each $21 rebate offered to a buyer, the number of sets sold will increase by 210 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.
b) How large rebate should the company offer to a buyer, in order to maximize its revenue?
c) If the weekly cost function is 81250+130x , how should it set the size of the rebate to maximize its profit?