Please help me answer the following question

Question 4. (30 marks) Consider maximizing utility where U (x, y) = a In rit B In r2 with the budget constraint piri + P212 - m. (a) Write down the Langrangian and find the first order conditions. (b) Solve for the optimal values of r1 72 and the Langrange Multiplier. Call these ri, x5, *. Show if rf and r; are homogenous in p1, p2 and m and to which degree. (c) Verify that you have found a maximum. (d) Find the indirect utility function. (e) What does A* represent in economic terms? (f) Verify Roy's identity holds in this case