#1) Bob is a utility maximizing consumer that consumes only candy bars (x) and ice cream sandwiches (y), both of which are nonnegative. Bob's preferences are given by the utility function, u(x, y) = x3y3. The price of candy bars is $3 per unit and the price of ice cream sandwiches is $6 per unit. Bob has a budget of $36 that he cannot exceed. Candy bars have a caloric intake of 400 calories per unit and ice cream sandwiches have a caloric intake of 200 calories per unit. For health reasons, Bob's consumption cannot exceed the recommended 2400 calorie constraint. a) Write out Bob's optimization problem. Identify all constraints. How many can be binding at the same time in any solution? Are there any that you expect not to bind in the solution (hint: inspect the objective function and graph the feasible region)? b) Write out the KKT Lagrangian associated with this problem in standard form. Derive the system of KKT first order conditions that characterize solution candidates. c) Carefully consider the system in b) and identify the optimal solution candidate and report the values of the relevant multipliers in the optimal solution. How do you interpret the Lagrange multiplier(s) at the optimal solution? d) Verify that the second order condition holds at the solution found in c) by running the appropriate Bordered Hessian test