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A manufacture has been selling 1950 television sets a week at $480 each. A market survey indicates that for each $10 rebate offered to a buyer, the number of sets sold will increase by 100 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 75000+120x , how should it set the size of the rebate to maximize its profit?