Suppose that a decision maker is choosing how much of goods 1 and 2 to consume. The quantities of each good are denoted by x1 and x2 respectively. Both goods have a unit cost of 1, and the consumer has a total budget of 5. The overall utility function of the decision maker is given by 2x 2 1 + 3x 2 2 . Thus, the decision maker's problem is max x1,x2 2x 2 1 + 3x 2 2 subject to x1 + x2 = 5 (a) (3 marks) Write down the Lagrangian for this problem. (b) (6 marks) Write down the first order conditions for the decision maker's problem and find the values of x1 and x2 which satisfy those first order conditions. (c) (6 marks) Check the second order conditions for the solution you found in part (b). Do these values of x1 and x2 solve the decision maker's problem