Chapter 14.3, Problem 2E

BuyFind*arrow_forward*

11th Edition

Ronald J. Harshbarger + 1 other

ISBN: 9781305108042

Textbook Problem

The manufacture of 1 unit of a product has a cost (in dollars) given by

*x* is the cost of 1 pound of one raw material, *y* is the cost of 1 pound of a second raw material, and *z* is the cost of 1 work-hour of labor.

(a) If the cost of the first raw material is $16 per pound, the cost of the second raw material is $8 per pound, and labor costs $18 per work-hour, what will it cost to produce 1 unit of the product?

(b) Find and interpret the partial derivative of C with respect to *x.*

**(a)**

To determine

**To calculate:** The cost to produce 1 unit of the product if the cost of the first raw material is $16 per pound, the cost of the second raw material is $8 per pound, and labor costs $18 per hour. The manufacture of 1 unit of a product has a cost (in dollars) given by *x* is the cost of 1 pound of one raw material, *y* is the cost of 1 pound of a second raw material, and *z* is the cost of 1 work-hour of labor.

Explanation

**Given Information:**

The manufacture of 1 unit of a product has a cost (in dollars) given by *x* is the cost of 1 pound of one raw material, *y* is the cost of 1 pound of a second raw material, and *z* is the cost of 1 work-hour of labor. Also, the cost of the first raw material is $16 per pound, the cost of the second raw material is $8 per pound, and labor costs $18 per hour.

**Calculation:**

Consider the problem, the manufacture of 1 unit of a product has a cost (in dollars) given by *x* is the cost of 1 pound of one raw material, *y* is the cost of 1 pound of a second raw material, and *z* is the cost of 1 work-hour of labor.

The provided function is

Also, the cost of the first raw material is $16 per pound, the cost of the second raw material is $8 per pound, and labor costs $18 per hour.

Thus,

**(b)**

To determine

**To calculate:** The partial derivative of *C* with respect to *x*. The manufacture of 1 unit of a product has a cost (in dollars) given by *x* is the cost of 1 pound of one raw material, *y* is the cost of 1 pound of a second raw material, and *z* is the cost of 1 work-hour of labor. Interpret the answer.

Sect-14.1 P-1CPSect-14.1 P-1ESect-14.1 P-2ESect-14.1 P-3ESect-14.1 P-4ESect-14.1 P-5ESect-14.1 P-6ESect-14.1 P-7ESect-14.1 P-8ESect-14.1 P-9E

Sect-14.1 P-10ESect-14.1 P-11ESect-14.1 P-12ESect-14.1 P-13ESect-14.1 P-14ESect-14.1 P-15ESect-14.1 P-16ESect-14.1 P-17ESect-14.1 P-18ESect-14.1 P-19ESect-14.1 P-20ESect-14.1 P-21ESect-14.1 P-22ESect-14.1 P-23ESect-14.1 P-24ESect-14.1 P-25ESect-14.1 P-27ESect-14.1 P-28ESect-14.1 P-29ESect-14.1 P-30ESect-14.1 P-31ESect-14.1 P-32ESect-14.1 P-33ESect-14.1 P-34ESect-14.1 P-35ESect-14.1 P-36ESect-14.1 P-37ESect-14.1 P-38ESect-14.2 P-1CPSect-14.2 P-2CPSect-14.2 P-3CPSect-14.2 P-4CPSect-14.2 P-5CPSect-14.2 P-1ESect-14.2 P-2ESect-14.2 P-3ESect-14.2 P-4ESect-14.2 P-5ESect-14.2 P-6ESect-14.2 P-7ESect-14.2 P-8ESect-14.2 P-9ESect-14.2 P-10ESect-14.2 P-11ESect-14.2 P-12ESect-14.2 P-13ESect-14.2 P-14ESect-14.2 P-15ESect-14.2 P-16ESect-14.2 P-17ESect-14.2 P-18ESect-14.2 P-19ESect-14.2 P-20ESect-14.2 P-21ESect-14.2 P-22ESect-14.2 P-23ESect-14.2 P-24ESect-14.2 P-25ESect-14.2 P-26ESect-14.2 P-27ESect-14.2 P-28ESect-14.2 P-29ESect-14.2 P-30ESect-14.2 P-31ESect-14.2 P-32ESect-14.2 P-33ESect-14.2 P-34ESect-14.2 P-35ESect-14.2 P-36ESect-14.2 P-37ESect-14.2 P-38ESect-14.2 P-39ESect-14.2 P-40ESect-14.2 P-41ESect-14.2 P-42ESect-14.2 P-43ESect-14.2 P-44ESect-14.2 P-45ESect-14.2 P-46ESect-14.2 P-47ESect-14.2 P-48ESect-14.2 P-49ESect-14.2 P-50ESect-14.2 P-51ESect-14.2 P-52ESect-14.2 P-53ESect-14.2 P-54ESect-14.2 P-55ESect-14.2 P-56ESect-14.3 P-1CPSect-14.3 P-2CPSect-14.3 P-3CPSect-14.3 P-1ESect-14.3 P-2ESect-14.3 P-3ESect-14.3 P-4ESect-14.3 P-5ESect-14.3 P-6ESect-14.3 P-7ESect-14.3 P-8ESect-14.3 P-9ESect-14.3 P-10ESect-14.3 P-11ESect-14.3 P-12ESect-14.3 P-13ESect-14.3 P-14ESect-14.3 P-15ESect-14.3 P-16ESect-14.3 P-17ESect-14.3 P-18ESect-14.3 P-19ESect-14.3 P-20ESect-14.3 P-21ESect-14.3 P-22ESect-14.3 P-23ESect-14.3 P-24ESect-14.3 P-25ESect-14.3 P-26ESect-14.3 P-27ESect-14.3 P-28ESect-14.3 P-29ESect-14.3 P-30ESect-14.4 P-1CPSect-14.4 P-2CPSect-14.4 P-3CPSect-14.4 P-4CPSect-14.4 P-1ESect-14.4 P-2ESect-14.4 P-3ESect-14.4 P-4ESect-14.4 P-5ESect-14.4 P-6ESect-14.4 P-7ESect-14.4 P-8ESect-14.4 P-9ESect-14.4 P-10ESect-14.4 P-11ESect-14.4 P-12ESect-14.4 P-13ESect-14.4 P-14ESect-14.4 P-15ESect-14.4 P-16ESect-14.4 P-17ESect-14.4 P-18ESect-14.4 P-19ESect-14.4 P-20ESect-14.4 P-21ESect-14.4 P-22ESect-14.4 P-23ESect-14.4 P-24ESect-14.4 P-25ESect-14.4 P-26ESect-14.4 P-27ESect-14.4 P-28ESect-14.4 P-29ESect-14.4 P-30ESect-14.4 P-31ESect-14.4 P-32ESect-14.4 P-34ESect-14.4 P-35ESect-14.4 P-36ESect-14.5 P-1CPSect-14.5 P-2CPSect-14.5 P-3CPSect-14.5 P-4CPSect-14.5 P-1ESect-14.5 P-2ESect-14.5 P-3ESect-14.5 P-4ESect-14.5 P-5ESect-14.5 P-6ESect-14.5 P-7ESect-14.5 P-8ESect-14.5 P-9ESect-14.5 P-10ESect-14.5 P-11ESect-14.5 P-12ESect-14.5 P-13ESect-14.5 P-14ESect-14.5 P-15ESect-14.5 P-16ESect-14.5 P-17ESect-14.5 P-18ESect-14.5 P-19ESect-14.5 P-20ESect-14.5 P-21ESect-14.5 P-22ESect-14.5 P-23ESect-14.5 P-24ESect-14.5 P-25ESect-14.5 P-26ECh-14 P-1RECh-14 P-2RECh-14 P-3RECh-14 P-4RECh-14 P-5RECh-14 P-6RECh-14 P-7RECh-14 P-8RECh-14 P-9RECh-14 P-10RECh-14 P-11RECh-14 P-12RECh-14 P-13RECh-14 P-14RECh-14 P-15RECh-14 P-16RECh-14 P-17RECh-14 P-18RECh-14 P-19RECh-14 P-20RECh-14 P-21RECh-14 P-22RECh-14 P-23RECh-14 P-24RECh-14 P-25RECh-14 P-26RECh-14 P-27RECh-14 P-28RECh-14 P-29RECh-14 P-30RECh-14 P-31RECh-14 P-32RECh-14 P-33RECh-14 P-34RECh-14 P-35RECh-14 P-36RECh-14 P-1TCh-14 P-2TCh-14 P-3TCh-14 P-4TCh-14 P-5TCh-14 P-6TCh-14 P-7TCh-14 P-8TCh-14 P-9TCh-14 P-10T

Finite Mathematics

Precalculus: Mathematics for Calculus (Standalone Book)

Intermediate Algebra

Understanding Basic Statistics

Finite Mathematics and Applied Calculus (MindTap Course List)

Probability and Statistics for Engineering and the Sciences

Essentials of Statistics for The Behavioral Sciences (MindTap Course List)

Calculus: Early Transcendental Functions

Calculus (MindTap Course List)

Essentials Of Statistics

Single Variable Calculus

Single Variable Calculus: Early Transcendentals, Volume I

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

Calculus: Early Transcendentals

Applied Calculus

Calculus: An Applied Approach (MindTap Course List)

Multivariable Calculus

Calculus (MindTap Course List)

Statistics for The Behavioral Sciences (MindTap Course List)

Elementary Technical Mathematics

Mathematical Excursions (MindTap Course List)

Elementary Geometry For College Students, 7e

Contemporary Mathematics for Business & Consumers

Trigonometry (MindTap Course List)

Elements Of Modern Algebra

Finite Mathematics for the Managerial, Life, and Social Sciences

Calculus of a Single Variable

Elementary Geometry for College Students

Calculus: Early Transcendental Functions (MindTap Course List)

Single Variable Calculus: Early Transcendentals

Study Guide for Stewart's Multivariable Calculus, 8th

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

Introduction To Statistics And Data Analysis