A monopolist manufactures and sells two competing products, call them I and II, that cost $32 and $23 per unit, respectively, to produce.

A monopolist manufactures and sells two competing products, call them I and II, that cost $32 and $23 per unit, respectively, to produce. The revenue from marketing x units of product I and y units of product II isR(x,y) = 100x+ 115y−0.04xy−0.1x2−0.2y2. Find the exact values of x and y that maximize the monopolist's profits.