QUESTION 1 Consider the standard utility maximization problem: max U =U (z,y) subject to where F, and F, denote the price of goods x and y. respectively, and B represents the consumer's available income. (a) Write the Lagrangian function and obtain the first-order conditions. (6 marks) (b) AssumethatU =zy, P, =1, B, =4and B = 120. Find A" along with the optimal levels of purchase x* and y*. Calculate U*. (10 marks) (e) Using the Bordered Hessian matrix, verify that the second-order con- ditions for a maximum are satisfied. (9 marks)