Use the method of Lagrange multipliers to optimize $f$ as indicated, subject to the given constraint(s).

Production is modeled by the Cobb Douglas production function $f(x, y)=200 x^{2} y^{\frac{1}{5}},$ 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.