Explanation Given Information: The productivity model at the company is P = 10 , 000 x 0.7 y 0.3 , P is the number of gadgets the company turns out per month, x is the number of employees at the company and y is the monthly operating budget in thousands of dollars, the number of workers is between 45 and 55 . The operating budget varies from $ 8 , 000 to $ 12 , 000 per month. Formula used: The value of the integral ∬ R f ( x , y ) d x d y is ∫ a b ( ∫ c ( x ) d ( x ) f ( x , y ) d y ) d x where the region R is defined by a ≤ x ≤ b and c ( x ) ≤ y ≤ d ( x ) . The average value of a function f ( x , y ) on the region R is f ¯ = 1 A ∬ R f ( x , y ) d x d y where A is the area of the region, A = ∬ R d x d y . Calculation: Consider the productivity model at the company is P = 10 , 000 x 0.3 y 0.7 , P is the number of gadgets the company turns out per month, x is the number of employees at the company and y is the monthly operating budget in thousands of dollars, the number of workers is between 45 and 55 . The operating budget varies from $ 8 , 000 to $ 12 , 000 per month. Let 10 , 000 x 0.7 y 0.3 = f ( x , y ) and the region is 45 ≤ x ≤ 55 and 8 ≤ y ≤ 12 , since y is represented in thousands of dollars. Thus, calculate ∬ R f ( x , y ) d x d y . Recall that the value of the integral ∬ R f ( x , y ) d x d y is ∫ a b ( ∫ c ( x ) d ( x ) f ( x , y ) d y ) d x where the region R is defined by a ≤ x ≤ b and c ( x ) ≤ y ≤ d ( x ) . Thus, ∬ R f ( x , y ) d x d y = ∫ 45 55 ( ∫ 8 12 10 , 000 x 0.7 y 0.3 d y ) d x . Simplify the integral ∫ 45 55 ( ∫ 8 12 10 , 000 x 0.7 y 0.3 d y ) d x with respect to y . ∫ 45 55 ( ∫ 8 12 10 , 000 x 0.7 y 0.3 d y ) d x = 10 , 000 ∫ 45 55 ( ∫ 8 12 x 0.7 y 0.3 d y ) d x = 10 , 000 ∫ 45 55 [ x 0.7 y 1.3 1.3 ] y = 8 12 d x = 10 , 000 ∫ 45 55 [ x 0.7 ( 12 1.7 1.3 − 8 1.7 1

7th Edition

ISBN: 9781337291408

Author: Stefan Waner, Steven Costenoble

Publisher: Brooks Cole

See similar textbooks

Concept explainers

Correlation

Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.

Linear Correlation

A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.

Regression Analysis

Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as p…

Videos

Question

Chapter 8.5, Problem 42E

To determine

To calculate: The average value of the number of gadgets the company can turn out per month where the productivity model at the company is P=10,000x0.7y0.3.

Expert Solution & Answer

Chapter 8 Solutions

Applied Calculus, Loose-leaf Version

Ch. 8.1 - For each function in Exercises 14, evaluate (a)...Ch. 8.1 - For each function in Exercises 14, evaluate (a)...Ch. 8.1 - For each function in Exercises 14, evaluate (a)...Ch. 8.1 - For each function in Exercises 14, evaluate (a)...Ch. 8.1 - For each function in Exercises 5-8, evaluate (a)...Ch. 8.1 - Prob. 6E Ch. 8.1 - For each function in Exercises 5-8, evaluate (a)...Ch. 8.1 - For each function in Exercises 5-8, evaluate (a)...Ch. 8.1 - Prob. 9E Ch. 8.1 - Prob. 10E

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

The average value of the number of gadgets the company can turn out per month where the productivity model at the company is P = 10 , 000 x 0.7 y 0.3 .

Solution Summary: The author calculates the average value of the number of gadgets a company can turn out per month based on the productivity model.

Concept explainers

Videos

To calculate: The average value of the number of gadgets the company can turn out per month where the productivity model at the company is P=10,000x0.7y0.3.

Chapter 8 Solutions