An outdoor outfitter estimates its total production of 60-meter climbing ropes is f(x,y) = 4x^0.75y^0.25, where x is the number of units of labor and y is the number of units of capital utilized. If $40,000 is available for labor and capital, and if the firm's cost are $100 per unit of labor and $200 per unit of capital, how many units of each will give the maximized production?

How many 60-meter ropes will be produced?

Use the Lagrange method.