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**stepho_145** A manufacture has been selling 1200 television sets a week @ $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 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 78,000+130x, how should it set the size of the rebate to maximize its Profits?