Let f (x, y) be any production function where x represents labor (costing $a per unit) and
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Let f (x, y) be any production function where x represents labor (costing $a per unit) and y represents capital (costing $b per unit). Assuming that $c is available, show that, at the values of x, y that maximize production,
Let F (x, y, λ) = f (x, y) + λ(c - ax - by). The result follows from (L-1) and (L-2).
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Related Book For 
Calculus And Its Applications
ISBN: 9780134437774
14th Edition
Authors: Larry Goldstein, David Lay, David Schneider, Nakhle Asmar
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