5.4. Question. (Constrained Optimization). Consider the two following constrained maximization. In each of them, determine which constraint (91 and 9) is binding and which one is non-binding. Assume x > 0 and y> 0. Hint: By using Lagrangian, find the constrained maximal of the two following functions (f and fa) subject to the two constraints. If the optimal solution lies on the boundary of a constraint, that constraint is binding and if does not lie on the boundary of a constraint, that constraint is non-binding (1) The first maximization f(x,y) = ln (x) + In (y) subject to 91: 3x + y s 30 and 92: x + 3y = 30 (2) The second maximization 12(x, y) = In (x) + y subject to 91 : 3x + y s 30 and 92: x + 3y