Production is modeled by the cobb douglas production

Question

Question: Production is modeled by the Cobb Douglas production function

f(x, y) = 200x^2/3y^1/3,

where x represents the number of units of labor, and y the number of units of capital. If each unit of labor costs $500 and each unit of capital $200, and the amount allocated to labor and capital is $300,000, use Lagrange multipliers to determine the number of units of labor and capital which maximizes the level of production.