A manufacturer's total production of a new product is P(L, K) = 1200L2/3K1/3 where L is the number of units of labor and K is the number of units of capital. A unit of labor costs $100, a unit of capital $400, and the total budget for labor and capital is $480,000. (a) To maximize production, how much should be spent on labor? $  160000       How much on capital? $  320000       (b) Find the value of the Lagrange multiplier. 252

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
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Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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A manufacturer's total production of a new product is

P(L, K) = 1200L2/3K1/3

where L is the number of units of labor and K is the number of units of capital. A unit of labor costs $100, a unit of capital $400, and the total budget for labor and capital is $480,000.

(a) To maximize production, how much should be spent on labor?
160000
 
 
 

How much on capital?
320000
 
 
 

(b) Find the value of the Lagrange multiplier.
252
 
 
 
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