申論題

4. John Mills - the proprietor of Mills Engine Company, a manufacturer of model air-plane engines - finds that it takes x units of labor and y units of capital to produce
f(x,y) = 100x^3/4y^1/4
units of the 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. (10分)