Question

4. Problems 2.4 Suppose you would like to maximizefxy)-xy, subject to the constraint that x and y are constrained to sum to 1. That is, xy 1 Instead of working through this maximization problem, however, you could also work through the dual problem to this, which is: Minimize x+ y subject to xy = 0.25 Hint: Assume x and y take only positive values The Lagrangian for this constrained minimization in the dual problem is Which of the following are the first order conditions for a critical point for the Lagrangian function L? Check all that apply. dl dL dx dy dL dL dr = 1 + x = 0 ▼ andy"= Solving the first order conditions for this Lagrangian yields x*- multiplier is i-Finally, this implies the minimum value offx*y*)-x*+y*- . This implies that the value of the Lagrangian The Lagrangian multiplier λ for this constrained minimization dual problem is constrained maximization, or "primal," problem. the Lagrangian multiplier in the corresponding

Answer 1