Problem

甲、計算、證明題：共 2 題，每題 10 分，共 20 分。須詳細寫出計算及證明過程，否則不予計分。

1. The production of $Q$ units of a commodity is related to the amount of labor $x$ and the amount of capital $y$ (in suitable units) expended by the equation $Q=f(x,y)=x^{3/4}y^{1/4}$. If an expenditure of 100 units is available for production, how should it be apportioned between labor and capital so that $Q$ is maximized?