Question
upstudy study bank question image url

The marginal cost of a product can be thought of as the cost of producing one additional unit of output. For example, if the marginal cost of producing the 50 th product is \( \$ 620 \), it cost \( \$ 6.20 \) to increase production from 49 to 50 units of output. Suppose the marginal cost \( C \) (in dollars) to produce \( x \) thousand mp3 players is given by the function \( C(x)=x^{2}-120 x+8400 \). A. How many players should be produced to minimize the marginal cost? B. What is the minimum marginal cost? A. To minimize the marginal cost, \( \square \) thousand mp3 players should be produced. B. The minimum marginal cost is \( \$ \square \)

Ask by Luna Montgomery. in the United States
Mar 15,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

A. To minimize the marginal cost, 60 thousand mp3 players should be produced. B. The minimum marginal cost is \$4800.

Solution

Sign in to Unlock Answers for Free!

A Learning Platform Trusted by Millions of Real Students and Teachers.

star-icon Unlock

Answered by UpStudy AI and reviewed by a Professional Tutor

The Deep Dive

To find the number of players that should be produced to minimize the marginal cost, we first need to take the derivative of the marginal cost function \( C(x) = x^2 - 120x + 8400 \). Setting the derivative \( C'(x) = 2x - 120 \) equal to zero gives us \( 2x - 120 = 0 \), leading to \( x = 60 \). So, to minimize the marginal cost, **60 thousand mp3 players should be produced**. To find the minimum marginal cost, we substitute \( x = 60 \) back into the original cost function: \( C(60) = (60)^2 - 120(60) + 8400 \). This calculates to \( C(60) = 3600 - 7200 + 8400 = 3600 \). Hence, **the minimum marginal cost is \( \$ 3600 \)**.

Related Questions

Latest Economics Questions

Try Premium now!
Try Premium and ask Thoth AI unlimited math questions now!
Maybe later Go Premium
Study can be a real struggle
Why not UpStudy it?
Select your plan below
Premium

You can enjoy

Start now
  • Step-by-step explanations
  • 24/7 expert live tutors
  • Unlimited number of questions
  • No interruptions
  • Full access to Answer and Solution
  • Full Access to PDF Chat, UpStudy Chat, Browsing Chat
Basic

Totally free but limited

  • Limited Solution
Welcome to UpStudy!
Please sign in to continue the Thoth AI Chat journey
Continue with Email
Or continue with
By clicking “Sign in”, you agree to our Terms of Use & Privacy Policy