A manufacture has been selling 1700 television sets a week at 420dollars each. A market survey indicates that for each 21 -dollarrebate offered to a buyer, the number of sets sold will increase by210 per week.

a) Find the demand function p(x), where x is the number of the television sets soldper week, assuming that p(x) is linear.

b) How large of a rebate should the company offer to a buyer, inorder to maximize its revenue?

c) If the weekly cost function is 119000 + 140 x, how should it set the size ofthe rebate to maximize its profit?