A manufacture has been selling \( 1700 \) television sets a week at \( \$ 360 \) each. A market survey indicates that for each \( \$ 20 \) rebate offered to a buyer, the number of sets sold will increase by \( 200 \) per week.
i. Find the demand function \( p ( x ) \) , where \( x \) is the number of the television sets sold per week.
\( p ( x ) = \)
ii. How large rebate should the company offer to a buyer, in order to maximize its revenue?
iii. If the weekly cost function is \( 102000 + 120 x \) , how should it set the size of the rebate to maximize its profit?