Consider a firm producing 2 goods, Good x and Good y. Let x and y be outputs of Good x and Good y, respectively. Suppose that the firm is facing the following cost function: TC(x, y) = 3x² + xy + 2y² + 424.

Further assume that the firm has estimated the demand functions for each product to equal: Demandx : Px = 92 - 2x Demandy : Py = 176 - 5y

Find the profit maximizing output of each good. Show your work. Make sure you prove that profit is, indeed, maximized.