A production function for a business follows the model P(L, K) = 0.5L0.7 K°-.3 over the course of one year, where P represents the total value of all products the company makes, L represents the value of the labor from employees, and K represents the value of all the company's assets (buildings, machines, etc.), where everything is measured in millions of dollars. a. Find and , and explain what they represent in this context. b. Evaluate the partial derivatives from part a when (L, K) = (3,2). If this was your business and your values, if you wanted to expand would it be better to expand in workforce (increase L) or expand in assets (increase K)?
A production function for a business follows the model P(L, K) = 0.5L0.7 K°-.3 over the course of one year, where P represents the total value of all products the company makes, L represents the value of the labor from employees, and K represents the value of all the company's assets (buildings, machines, etc.), where everything is measured in millions of dollars. a. Find and , and explain what they represent in this context. b. Evaluate the partial derivatives from part a when (L, K) = (3,2). If this was your business and your values, if you wanted to expand would it be better to expand in workforce (increase L) or expand in assets (increase K)?
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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Transcribed Image Text:A production function for a business follows the model P(L, K) = 0.5L0.7 K°-.3 over
the course of one year, where P represents the total value of all products the
company makes, L represents the value of the labor from employees, and K
represents the value of all the company's assets (buildings, machines, etc.), where
everything is measured in millions of dollars.
a. Find and
, and explain what they represent in this context.
b. Evaluate the partial derivatives from part a when (L, K) = (3,2). If this was
your business and your values, if you wanted to expand would it be better to
expand in workforce (increase L) or expand in assets (increase K)?
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