calculus application to economics

A manufacture has been selling 1650 television sets a week at 480 each. A market survey indicates that for each 19 rebate offered to a buyer, the number of sets sold will increase by 190 per week.

a) Find the demand function http://hosted2.webwork.rochester.edu...d3c42db151.png, where http://hosted2.webwork.rochester.edu...dd0b8b8e91.png is the number of the television sets sold per week.

http://hosted2.webwork.rochester.edu...9b23380b61.png

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

c) If the weekly cost function is http://hosted2.webwork.rochester.edu...989be49931.png, how should it set the size of the rebate to maximize its profit?