Question

The cost, in dollars, of producing x belts is given by C(x) = 508 + 12x - 0.072x^2. The revenue, in dollars, of producing and selling x belts is given by R(x) = 40x^(2/3). Find the rate at which average profit is changing when 484 belts have been produced and sold. When 484 belts have been produced, the average profit is changing at (.........) dollars per belt for each additional belt.

Name: the cost in dollars of producing x belts is given by cx 508 12x 0072x2 the revenue in dollars of producing and selling x belts is given by rx 40x23 find the rate at which average profit is c 48049
Uploaded: 2022-06-04T22:46:17-08:00
Duration: 3 min 54 s
Channel: Vishal Parmar
Description: the cost in dollars of producing x belts is given by cx 508 12x 0072x2 the revenue in dollars of producing and selling x belts is given by rx 40x23 find the rate at which average profit is c 48049

          The cost, in dollars, of producing x belts is given by C(x) = 508 + 12x - 0.072x^2. The revenue, in dollars, of producing and selling x belts is given by R(x) = 40x^(2/3). Find the rate at which average profit is changing when 484 belts have been produced and sold.
When 484 belts have been produced, the average profit is changing at (.........) dollars per belt for each additional belt.

Added by Jim A.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Vishal Parmar

06/04/2022

Step 1

Given: Cost function, \(C(x) = 508 + 12x - 0.072x^2\) Revenue function, \(R(x) = 40x^{2/3}\) Profit function, \(P(x) = R(x) - C(x)\) Substitute the given functions: \(P(x) = 40x^{2/3} - (508 + 12x - 0.072x^2)\) \(P(x) = 40x^{2/3} - 508 - 12x + 0.072x^2\) Show more…

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The cost, in dollars, of producing x belts is given by C(x) = 508 + 12x - 0.072x^2. The revenue, in dollars, of producing and selling x belts is given by R(x) = 40x^(2/3). Find the rate at which average profit is changing when 484 belts have been produced and sold. When 484 belts have been produced, the average profit is changing at (.........) dollars per belt for each additional belt.