### Production Function AnalysisA manufacturer has modeled its yearly production function $ P $ (the monetary value of its entire production in millions of dollars) using a Cobb-Douglas function:\[ P(L, K) = 1.47L^{0.65}K^{0.35} \]where $ L $ is the number of labor hours (in thousands) and $ K $ is the invested capital (in millions of dollars). #### Problem StatementFind $ P(100, 60) $ and interpret it. (Round your answers to one decimal place.)\[ P(100, 60) = \boxed{ } \]So when the manufacturer invests $ \boxed{ } million in capital and \boxed{ } thousand hours of labor are completed yearly, the monetary value of the production is about $ \boxed{} million.

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A manufacturer has modeled its yearly production function P (the monetary value of its entire production in millions of dollars) as a Cobb-Douglas function P(L, K) = 1.47L0.65K0.35 where L is the number of labor hours (in thousands) and K is the invested capital (in millions of dollars). Find P(100, 60) and interpret it. (Round your answers to one decimal place.) P(100, 60) = | monetary value of the production is about $ , so when the manufacturer invests $ million in capital and thousand hours of labor are completed yearly, the million.

A manufacturer has modeled its yearly production function P (the monetary value of its entire production in millions of dollars) as a Cobb-Douglas function P(L, K) = 1.47L0.65K0.35 where L is the number of labor hours (in thousands) and K is the invested capital (in millions of dollars). Find P(100, 60) and interpret it. (Round your answers to one decimal place.) P(100, 60) = | monetary value of the production is about $ , so when the manufacturer invests $ million in capital and thousand hours of labor are completed yearly, the million.

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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Concept explainers

Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.

Question

### Production Function Analysis

A manufacturer has modeled its yearly production function $ P $ (the monetary value of its entire production in millions of dollars) using a Cobb-Douglas function:

\[ P(L, K) = 1.47L^{0.65}K^{0.35} \]

where $ L $ is the number of labor hours (in thousands) and $ K $ is the invested capital (in millions of dollars).

#### Problem Statement

Find $ P(100, 60) $ and interpret it. (Round your answers to one decimal place.)

\[ P(100, 60) = \boxed{ } \]

So when the manufacturer invests $ \boxed{ } million in capital and \boxed{ } thousand hours of labor are completed yearly, the monetary value of the production is about $ \boxed{} million.

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