Question

3. Problems 2.3 Suppose that f(x,y)=xy, with the constraint that x and y are constrained to sum to 1. That is, x +y = 1 Given this constraint, which of the following functions of x is equivalent to the original functionfx,y)=xy? f (x) = x2 f (x) = 1-r f (x) -x-x2 f(x) = x + x2 using the first order condition that f . (x) = 0, the value of x that maximizes f(x) (andfx,y)) is x- corresponding value of y that maximizesfx,y) is y" - second derivative off (x),f(A) = , evaluated at x*, is equal tof. (x*) = ▼ . Given this value of x", the ▼ . This means that the maximum value off(x,y) isf(x)* ▼ "The ▼ , which satisfies the second order condition for a maximum The langrange method can also be used to solve this constrained maximization problenm The langrangian for this constrained maximization problem is Which of the following are the first order conditions for a critical point for the langranian function L? Check all that apply dL dy dL dL dL Solving the first order conditions for this Lagra nian yields x* multiplier λ = ▼ andy*- ▼ . This implies that the value of the langrange ▼ . Finally, the maximum value offix*.y*)-x*y* In order for the second order condition for a critical point to be satisfied, fiif2 2-2h2hfz +fz2h2 at the critical point.

Answer 1