Given prices for two goods PX = 2 and PY = 3 and a budget of $120 a consumer is trying to maximize the utility function U(X, Y ) = 2X^0.3Y^0.7 Use the Lagrange method to solve this problem, but don’t worry about the second order conditions (if you wish, you can actually check that the MRS is decreasing and this utility function is well behaved). a) Write and solve the utility maximization problem subject to the budget constraint. What is the resulting value of the utility function? b) Write and solve the dual problem. Do you get the same optimal solution (the same optimal combination of X and Y)? What is the resulting expenditure? Does that match the budget of your original (primal) problem?