A manufacturer produces bolts of a fabric with a fixed width. The quantity q of this fabric (measured in metres) that is sold is a function of the selling price p (in dollars per metre), that is q = f(p) for some function f. Then the total revenue earned with selling price p is R(p) = pf(p).

(a) What does it mean to say that f(20) = 10000 and f′(20) = −350?

(b) Assuming these values for f(20) and f′(20), find R′(20) and interpret your answer.
asked Sep 15, 2016 in Calculus Answers by anonymous

Your answer

Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:

To avoid this verification in future, please log in or register.

1 Answer

a) The quantity q, in other words metres of fabric, is 10000m when the price is $20 per metre.

f'(20) = -350 means that at the point where the price is $20/m the quantity is decreasing at the rate of 350 m per unit price change. In other words, if the unit price decreases to, say, $19/m, then the quantity increases. If the unit price increases then the quantity decreases.

b) The revenue is how much the manufacturer will get from the sale of q metres of fabric when the cost to the customer is $20/m. 20 * 10000=200000 is the revenue from the sale. R'(20)=20f'(20)=20 * -350=-7000.



answered Sep 16, 2016 by Rod Top Rated User (486,900 points)
Welcome to MathHomeworkAnswers.org, where students, teachers and math enthusiasts can ask and answer any math question. Get help and answers to any math problem including algebra, trigonometry, geometry, calculus, trigonometry, fractions, solving expression, simplifying expressions and more. Get answers to math questions. Help is always 100% free!
79,816 questions
83,634 answers
66,552 users