Question

An accessories company finds that the cost and revenue, in dollars, of producing x belts is given by C(x) = 710 + 30x - 0.061x^2 and R(x) = 25x^(9/10) respectively. Determine the rate at which the accessories company's average profit per belt is changing when 173 belts have been produced and sold. First, find the rate at which the average profit is changing when x belts have been produced. P'(x) = nothing When 173 belts have been produced and sold, the average profit is changing at nothing dollars per belt for each additional belt. (Round to four decimal places as needed.)

          An accessories company finds that the cost and revenue, in dollars, of producing x belts is given by C(x) = 710 + 30x - 0.061x^2 and R(x) = 25x^(9/10) respectively. Determine the rate at which the accessories company's average profit per belt is changing when 173 belts have been produced and sold.

First, find the rate at which the average profit is changing when x belts have been produced. P'(x) = nothing

When 173 belts have been produced and sold, the average profit is changing at nothing dollars per belt for each additional belt.

(Round to four decimal places as needed.)

Show more…

Added by Alex B.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Donna Densmore

02/18/2023

Step 1

To find the rate at which the average profit is changing when 173 belts have been produced and sold, Show more…

Show all steps

lock

Thanks for your feedback!

An accessories company finds that the cost and revenue, in dollars, of producing x belts is given by C(x) = 710 + 30x - 0.061x^2 and R(x) = 25x^(9/10) respectively. Determine the rate at which the accessories company's average profit per belt is changing when 173 belts have been produced and sold. First, find the rate at which the average profit is changing when x belts have been produced. P'(x) = nothing When 173 belts have been produced and sold, the average profit is changing at nothing dollars per belt for each additional belt. (Round to four decimal places as needed.)

Play audio

Feedback

Powered by NumerAI

Donna Densmore and 95 other subject Calculus 1 / AB educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Recommended Videos

Recommended Textbooks

Transcript

00:01 And cost function for a particular company.

00:03 And it wants to know about the average profit.

00:06 So the first thing we need to do is find our profit.

00:09 Profit is going to be our revenue minus our cost.

00:12 So i'm going to say 25x to the 9th over 10 minus.

00:16 And i want to go ahead and wrap this in parentheses when i subtract it and get 710 minus 30x plus 061x squared.

00:27 So there's our profit function.

00:28 But they're talking about average profit.

00:31 So we need to take each piece and we need to put it over x.

00:34 Because the profit per item, we have x items.

00:39 We're going to be dividing the total profit by x.

00:42 So we're going to simplify this to be 25x to the 8th over 10, minus 710 over x, minus 30 plus 0 .061x.

00:54 So there's going to be our average profit, not prime average.

00:58 We want to know how the average profit is changing, which means we now need to take its derivative.

01:05 So i'm going to say this is, i'm going to rewrite this now.

01:07 It's 25 over 10.

01:12 So i don't know why that's not reduced.

01:16 So i'm going to go ahead and reduce 25 over 10...

Ace is your personal tutor. It breaks down any question with clear steps so you can learn.

Start Using Ace

Continue solving this problem

Create a free account to:

View full step-by-step solution
Ask follow-up questions with Ace AI
Save progress and study later