A self-employed salesperson has its occupation area defined in part by the edge of a lake, which can be described, in terms of $x$ and $y$ coordinates, as the region bounded by the curve $y=x^2$ (the edge of the lake) and the lines $y=0$ and $x=3$ and , where $x$ and $y$ are in kilometers.
He notes that the number of products $S(x,y)$ he can sell at each point $(x,y)$ in his area of expertise is given by the function
$$S(x,y)= 4x^2−16x+4y^2−4y+20.$$
At what point does he sell more products? At what point does it sell less products? What quantities are sold in each case?
I'm having trouble trying to solve this problem. I've tried to use partial derivatives, but without success. Thanks for the help!
