# 4 ECON 2400A Winter 2016 Instructor: M. Vesselovsky Distributed: Mar 31 1. Due: April 7 Find the maximum value of : f (x,y) = x + 2y + 3z s.t. x - y + z = 1 and x2 + y2 = 1 2. Solve the following problem: max f(x,y) = xy s.t. x + y2 2 and x, y 0 Note that the global maximum exists for a continuous function on a closed and bounded set, so you just have to find it, not prove its existence. 3. Consider the problem: Max U (x, y) = 100 - (x - 1)2 - y2 subject to: x2 + y2 4 Prove that U (x, y) is concave. Write down the Kuhn-Tucker conditions for the solution of the problem. Find the possible solution(s). 4. Solve the differential equations with explicit solutions and intervals of validity: a) b) c)