In Example 13.3 we showed how a Pareto efficiency exchange equilibrium can be described as the solution to a constrained maximum problem. In this problem we provide a similar illustration for an economy involving production. Suppose that there is only one person in a two-good economy and that his or her utility function is given by U(x, y). Suppose also that this economy's production possibility frontier can be written in implicit form as T(x, y) 0. a. What is the constrained optimization problem that this economy will seek to solve if it wishes to make the best use of its available resources? b. What are the first-order conditions for a maximum in this situation? c. How would the efficient situation described in part (b) be brought about by a perfectly competitive system in which this individual maximizes utility and the firms underlying the production possibility frontier maximize profits. d. Under what situations might the first-order conditions described in part (b) not yield a utility maximum