II) Consider the problem of a consumer who must choose between two types of goods, good 1 (x1) and good 2 (X2) costing respectively p, and p2 per unit. He is endowed with an income m and has a quasi-concave utility function u defined by u(x1, $2 ) = 5lnx1 + 3Inc2. 1. Write down the problem of the consumer. * mark 2. Determine the optimal choice of good 1 and good 2, of = 1 (P1, P2, m) and x2 = $2 (P1, P2, m). 3 marks 3. Find the optimal amounts of good 1 and good 2 the consumer will choose if p1 = 1, p2 = 3 and m = 10. 1 mark III) Consider the optimization problem of the objective function