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Maximizing Production Suppose a company can manufacture P(x, y) units of a certain product by utilizing x units of labor and y units of capital. Furthermore, suppose the unit cost of labor and the unit cost of capital are p and q dollars, respectively (p > 0, q > 0 ). Finally, suppose that the management of the company has allocated C dollars for the manufacture of the product. Use the method of Lagrange multipliers to show that at the maximum level of production.
where x* and y* are the units of labor and capital, respectively, used at that level, and Px (x*, y*) and Py(x*, y*) are not both zero.
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Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage