For our function, it is easy to calculate that D = 36xy - 9. Thus at the point (0,0) we have D < 0 indicating a saddle and at (1,1) we have D = 27 > 0 as well as fxx(1,1) = - 6 < 0 which implies that (1,1) s a local maximum. Hence, to maximize profit we should sell one (thousand) of each of the two products. This will result in a net profit of f(1,1) = 1 million dollars.