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106 台聯大微積分(A2) 第 7 題

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106學年度 · 106微積分A2 · 第 7 題

題目

Problem

甲、填充題:共 8 題,每題 8 分,共 64 分。請在答案卷上列出題號依序作答。

  1. The Cobb-Douglas production function for a software manufacturer is given by f(x,y)=100x3/4y1/4f(x,y)=100x^{3/4}y^{1/4} where xx represents the units of labor (at $150 per unit) and yy represents the units of capital (at $250 per unit). The total cost of labor and capital is limited to $50,000. Find xx and yy that will yield the maximum production level for this manufacturer. Answer : \underline{\quad(1)\quad}

解答

解法一

Cobb—Douglas 指數 3/4:1/43/4:1/4 表示最適預算分配為勞力與資本支出 3:13:1。故勞力支出 3750037500、資本支出 1250012500,即

x=250,y=50.\boxed{x=250,\qquad y=50}.