Problem

3. A manufacturer finds that it takes $x$ units of labor and $y$ units of capital to produce $f(x,y)=100x^{3/4}y^{1/4}$ units of product. If a unit of labor costs $100, a unit of capital costs $200, and $200,000 is budgeted for production, determine how many units should be expended on labor and how many units should be expended on capital in order to maximize production.