PROBLEM SET #4 1. Consider the optimization problem max f(x,y) T,y subject to ar+by+c=0 where f:R? = R is a continuously differentiable function and ab # 0. Check whether the following statements are TRUE or FALSE a. We can apply the Weirstrass theorem to show that a solution (z*, y*) exists for this constrained optimization problem (5 pts) b. If (z*,y*) is a solution to this problem, then there exists \\* such that (z*,y*, \\*) satisfy the Lagrange first order conditions. (5 pts) 2. Solve the following maximization problem max Ty x,y subject to x? 4+ y? = 22 where > 0 is a constant. Make sure to include an argument as to why the Lagrange method should work (15 pts)