For this question, consider that the letter "A" denotes the last 4 digits of your student number. That is, for example, if your student number is: 12345678, then A = 5678. Suppose that the consumer has a utility function given by U(X, Y) = X0,2yo,8. The prices of goods X and Y are given by px = 4 TL and py = 2 TL. The total budget the consumer has is given by I = A TL. a. Write down the consumer's optimization problem (formally, as we wrote in the lectures) b. Apply the Lagrangian method. Find the necessary condition (NC) for the consumer's optimization problem. Then find the values of X and Y that maximize consumer's utility. Illustrate your results by using a graph. d. In the graph you drew for part (c), mark a consumption bundle that is not optimal (i.e. does not satisfy the NC) and discuss why it is not optimal