Concept explainers
A manufacturer produces bolts of a fabric with a fixed width. The quantity q of this fabric (measured in yards) that is sold is a function of the selling price p (in dollars per yard), so we can write q = f(p). Then the total revenue earned with selling price p is R(p) = pf(p).
(a) What does it mean to say that f(20) = 10,000 and f'(20) = –350?
(b) Assuming the values in part (a), find R'(20) and interpret your answer.
(a)
To describe: The meaning of
Explanation of Solution
The value
The value
(b)
To find: The value of
Explanation of Solution
Given:
The function
The values
Derivative rule:
(1) Product Rule:
(2) Power rule:
Calculation:
Obtain the value of
The derivative of the function
Apply the product rule (1) and the power rule (2),
Thus, the derivative of the function
Substitute 20 for p in
Substitute the value
The value of
That is, if the value of selling price is increase then the revenue is increases.
Therefore, the Revenue increases instaneously by $3000 for every $1 increase in price per yard.
Chapter 3 Solutions
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