Consider the function f = 31-x-y - z I. Write down the FOC [1.5 marks] II. Using the FOCs show that the solution to the optimization problem exists, note this question is not asking that you work out the solution, it only requires that you show it exist (hint: show that the system of linear equations has a unique solution) [1.5 marks] III. IV. Solve the system of equations that represents the FOC for the optimal values of choice variables x*, y*, z* [3 marks] Determine if the optimal point (if it exists) is a maximum or a minimum (use the bordered Hessian matrix) [4 marks] V. What is the optimal value of f* of [2 marks] VI. Given the fact that the hessian matrix in IV is a matrix of constants, what can you say about global/local convexity/concavity of the objective function f [3 marks]