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High School Math Calculus Calculus: Graphical, Numerical, Algebraic

The average cost of producing 100 machines.

The average cost of producing 100 machines.

Calculus: Graphical, Numerical, Algebraic

Calculus: Graphical, Numerical, Algebraic

3rd Edition

ISBN: 9780133688399

Author: Finney, Ross L.

Publisher: Pearson/Prentice Hall

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Question

Chapter 3.4, Problem 27E

a.

To determine

To calculate: The average cost of producing 100 machines.

a.

Expert Solution

Answer to Problem 27E

The correct answer is 90.

Explanation of Solution

Given information: In the question, dollar cost of producing x washing machine is given. c(x)=2000+100x−0.1x2 Using this we will find the solution of given questions.

Calculation:By formula we can find, average cost of producing 100 washing machines.

cavg.=total cost producing by washingmachinetotal productioncavg.=c(100)−c(0)100−0=11000−2000100=90010=90

Thus, the correct answer is 90.

b.

To determine

To calculate: The marginal cost when 100 machines are produced.

b.

Expert Solution

Answer to Problem 27E

The correct answer is 80.

Explanation of Solution

Given information: In the question, dollar cost of producing x washing machine is given. c(x)=2000+100x−0.1x2 Using this we will find the solution of given questions.

Calculation:

Find the marginal cost, by using differentiation method

c(x)=2000+100x−0.1x2dc(x)dx=100−0.2xat x=100,dc(x)dx=100−20=80.

Thus, the correct answer is 80.

c.

To determine

To calculate: c(101)−c(100)=dc(x)dxat x=100

c.

Expert Solution

Answer to Problem 27E

The correct answer c(101)−c(100)=79.9.

Explanation of Solution

Given information: In the question, dollar cost of producing x washing machine is given. c(x)=2000+100x−0.1x2 Using this we will find the solution of given questions.

Calculation:

To find cost of 100 washing machines, we will put x=100 in given equation.

c(x)=2000+100x−0.1x2x=100c(100)=2000+10000−1000c(100)=11,000

Similarly, c(101)=11,079.9

Find the difference between c(101) and c(100).

c(101)−c(100)=79.9.

See the above value is approximately equal to marginal cost of 100 washing machines.

Thus, the correct answer is c(101)−c(100)=79.9.

Chapter 3.4, Problem 26E

Chapter 3.4, Problem 28E

Chapter 3 Solutions

Calculus: Graphical, Numerical, Algebraic

Ch. 3.1 - Prob. 1QR Ch. 3.1 - Prob. 2QR Ch. 3.1 - Prob. 3QR Ch. 3.1 - Prob. 4QR Ch. 3.1 - Prob. 5QR Ch. 3.1 - Prob. 6QR Ch. 3.1 - Prob. 7QR Ch. 3.1 - Prob. 8QR Ch. 3.1 - Prob. 9QR Ch. 3.1 - Prob. 10QR

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