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
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
Section: Chapter Questions
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?
$
How much on capital?
$
(b) Find the value of the Lagrange multiplier.
$
160000
How much on capital?
$
320000
(b) Find the value of the Lagrange multiplier.
252
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