Suppose that the cost (in dollars) for a company to produce x pairs of a new line of jeans is described by the formula below. C(x) = 4000 + 5x + 0.01x^2 + 0.0002x^3 (a) Find the marginal cost function. C'(x) = (b) Find C'(60). (c) Find the actual cost of manufacturing the 61st pair of jeans. (Round your answer to two decimal places.) $
Added by Brandy L.
Close
Step 1
Given: $C(x) = 4000 + Sx + 0.01x^2 + 0.0002x^3$ Taking the derivative: $C'(x) = 0 + S + 0.02x + 0.0006x^2$ Therefore, the marginal cost function is: $C'(x) = S + 0.02x + 0.0006x^2$ ** Show more…
Show all steps
Your feedback will help us improve your experience
Taran S and 60 other Calculus 1 / AB educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Suppose that the cost (in dollars) for a company to produce $ x $ pairs of a new line of jeans is $ C(x) = 2000 + 3x + 0.01x^2 + 0.0002x^3 $ (a) Find the marginal cost function. (b) Find $ C'(100) $ and explain its meaning. What does it predict? (c) Compare $ C'(100) $ with the cost of manufacturing the 101st pair of jeans.
Suman Saurav T.
Suppose that the cost (in dollars) for a company to produce x pairs of a new line of jeans is C(x) = 4,000 + 4x + 0.02x^2 + 0.0001x^3. (a) Find the marginal cost function. (b) Find C'(140). What does it predict? It predicts the tax of the 140th pair. It predicts the approximate cost of the 140th pair. It predicts the cost difference between the 140th and 141st pair. It predicts the approximate cost of the 141st pair. It predicts the cost of 4,000 pairs. (c) Find the actual cost of manufacturing the 141st pair of jeans. (Round your answer to two decimal places.)
Gregory H.
Marginal cost Suppose that the dollar cost of producing $x$ washing machines is $c(x)=2000+100 x-0.1 x^{2} .$ a. Find the average cost per machine of producing the first 100 washing machines. b. Find the marginal cost when 100 washing machines are produced. c. Show that the marginal cost when 100 washing machines are produced is approximately the cost of producing one more washing machine after the first 100 have been made, by calculating the latter cost directly.
Derivatives
The Derivative as a Rate of Change
Recommended Textbooks
Calculus: Early Transcendentals
Thomas Calculus
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD