The demands for a monopolists two products are determined

Question

Question: The demands for a monopolist's two products are determined by the equations

p = 25 - x, q = 24 - 2y

where p and q are prices per unit of the two goods, and x and y are the corresponding quantities. The costs of producing and selling x units of the first good and y units of the other are

C(x, y) = 3x² + 3xy + y²

(a) Find the monopolist's profit π(x, y) from producing and selling x units of the first good and y units of the other.

(b) Find the values of x and y that maximize π(x, y). Verify that you have found the maximum profit.