Consider the production possibility frontier for a simple two-good (closed) economy. Quantities of good x produced are plotted on the horizontal axis. Quantities of good y produced are plotted on the vertical axis. Suppose that the production of both x and y depends only on labor input and that the production functions for these goods are: x = f(lx) = lx and y = f(ly) = ly. Total labor supply is limited by: lx + ly = 100. The typical individual’s utility function is given by U(x,y) = x·y. The equilibrium quantity of good x produced/consumed is how much and the equilibrium quantity of good y produced/consumed is how much? (NOTE: Write your answer in number format, with 2 decimal places of precision level; do not write your answer as a fraction. Add a leading zero and trailing zeros when needed. HINTS: First derive the production possibility frontier equation) Show all steps.