Solve the Problem $P$ Of a Factory During One Time Period Is Modeled By During

Solve the problem.
-The production level $P$ of a factory during one time period is modeled by $P(x, y) =K x^{1 / 2} y^{1 / 2}$ where $\mathrm{K}$ is a positive integer, $\mathrm{x}$ is the number of units of labor scheduled and $\mathrm{y}$ is the number of units of capital invested. If labor costs $\$ 400 /$ unit, capital costs $\$ 600 /$ unit and the owner has $\$ 1,800,000$ available for one time period, what amount of labor and capital would maximize production?

A) 1500.0 units of labor and 2250.0 units of capital
B) 4500.0 units of labor and 3000.0 units of capital
C) 1800.0 units of labor and 1285.7 units of capital
D) 2250.0 units of labor and 1500.0 units of capital