New machines are supplied on the market, on the basis of the statistical analyzes of the data, we have been able to evaluate the demand functions of these machines which are independent; the prices are respectively: p1 = 24-2x1 and P230-3x2? Where x1 and x2 are expected demands for prices P1 and P2? The 2 machines are manufactured with the same facilities so that their production costs can be expressed by the same function: C (x1, x2) = = f(x) = x21+2x1x2+x22+15?

We are asked to determine the quantities x1 and x2, the prices P1 and P2 which give maximum profit?