Assuming that m q24a2p find the utility-maximizing demand

Question

Question: (a) Assuming that m > q²/4a²p, find the utility-maximizing demand functions x∗(p, q, m, a) and y∗(p, q, m, a), as well as the indirect utility function U∗(p, q, m, a) = x∗ + ay∗, for the problem, max √(x) + ay subject to px + qy = m

(b) Find all four partials of U∗(p, q, m, a) = x∗ + ay∗ and verify the envelope theorem.