1) Find the solution of the following objective function. For each problem, confirm that the optimum satisfies the Kuhn-Tucker conditions and describe whether the constraint is binding. a) Minimize the cost function C (x , y) = 5x2 - 80x + y2 -32y subject to the constraints x, y > 0 and x + y> 20. b) Maximize the profit function P (x , y) =50x + 10y subject to the constraints x, y 2 0 and x-y