A manufacture has been selling 1400 television sets a week at 420 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 demand function p(x), where x is the number of the television sets sold per week.
b) How large rebate should the company offer to a buyer, in order to maximize its revenue?
c) If the weekly cost function is 98000+140x, how should it set the size of the rebate to maximize its profit?