A perfectly competitive firm produces 2 goods, X and Y which are sold at $0.99 and $1.25 respectively. The manager thinks that the total cost function is:
TC = 2 + 0.1q + 0.15r +0.05q² +0.12r² + 0.025qr
where q and r are the outputs of good X and good Y respectively.

a) Find the total revenue function and the marginal revenue functions for both products
b) Find the optimal values of q and r along with maximum profit
c) Use the second order conditions to determine whether profit is maximised at this point