The Cobb$-$Douglas production function for a particular product is $N(x,y)=60x^{0\mathrm{.}6}{y}^{0\mathrm{.}4},$ where $x$ is the number of units of labor and $y$ is the number of units of the product. Each unit of labor costs $$60$ and each unit of capital costs $$80.$

If $$200,000$ is budgeted for production of the product, determine how that amount should be allocated to maximize production.

Production will be maximized when using units of labor and capital.