Science:Math Exam Resources/Courses/MATH105/April 2010/Question 04

MATH105 April 2010
Other MATH105 Exams

Question 04

The production function for a firm is

$\displaystyle f(x,y)=5x^{2/3}y^{1/3},$ where $x$ and $y$ are the number of units of labour and capital utilized respectively. Suppose that labour costs $108 per unit and capital costs$2 per unit and that the firm decides to produce 600 units of goods. Use Lagrange multipliers to determine the amounts of labour and capital that should be utilized in order to minimize cost. You need not show that your solution minimizes the cost.

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