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 to revenue earned with selling price p is R(p) = pf(p). (a) What does it mean to say that f(15) = 10,000 in the context of this problem? O When the price of fabric is $15/yard, 10,000 yards will be sold. O There are 10,000 total yards of fabric and $425 to spend on it. O When the price of fabric is $425/yard, 15 yards will be sold. O There are 425 total yards of fabric and $15 to spend on it. O When the price of fabric is $15/yard, 425 yards will be sold. What does it mean to say that f'(15) = -425 in the context of this problem? O As the price of the fabric increases past $15/yard, the amount of fabric which will be sold is decreasing at a rate of 425 yards per (dollar per yard). O As the price of the fabric increases past $425/yard, the amount of fabric which will be sold is increasing at a rate of 15 yards per (dollar per yard). O As the price of the fabric decreases past $425/yard, the amount of fabric which will be sold is decreasing at a rate of $10,000 per (dollar per yard). O As the price of the fabric decreases past $15/yard, the amount of fabric which will be sold is increasing at a rate of $425 per (dollar per yard). O As the price of the fabric decreases past $15/yard, the amount of fabric which will be sold is increasing at a rate of 10,000 yards per (dollar per yard). (b) Assuming the values in part (a), find R'(15). R'(15) =
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 to revenue earned with selling price p is R(p) = pf(p). (a) What does it mean to say that f(15) = 10,000 in the context of this problem? O When the price of fabric is $15/yard, 10,000 yards will be sold. O There are 10,000 total yards of fabric and $425 to spend on it. O When the price of fabric is $425/yard, 15 yards will be sold. O There are 425 total yards of fabric and $15 to spend on it. O When the price of fabric is $15/yard, 425 yards will be sold. What does it mean to say that f'(15) = -425 in the context of this problem? O As the price of the fabric increases past $15/yard, the amount of fabric which will be sold is decreasing at a rate of 425 yards per (dollar per yard). O As the price of the fabric increases past $425/yard, the amount of fabric which will be sold is increasing at a rate of 15 yards per (dollar per yard). O As the price of the fabric decreases past $425/yard, the amount of fabric which will be sold is decreasing at a rate of $10,000 per (dollar per yard). O As the price of the fabric decreases past $15/yard, the amount of fabric which will be sold is increasing at a rate of $425 per (dollar per yard). O As the price of the fabric decreases past $15/yard, the amount of fabric which will be sold is increasing at a rate of 10,000 yards per (dollar per yard). (b) Assuming the values in part (a), find R'(15). R'(15) =
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter4: Calculating The Derivative
Section4.4: Derivatives Of Exponential Functions
Problem 56E
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Q12. Please answer all the parts to this question
Transcribed Image Text: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(15) = 10,000 in the context of this problem?
When the price of fabric is $15/yard, 10,000 yards will be sold.
There are 10,000 total yards of fabric and $425 to spend on it.
When the price of fabric is $425/yard, 15 yards will be sold.
There are 425 total yards of fabric and $15 to spend on it.
When the price of fabric is $15/yard, 425 yards will be sold.
(b)
What does it mean to say that f'(15) = -425 in the context of this problem?
As the price of the fabric increases past $15/yard, the amount of fabric which will be sold is decreasing at a rate of 425 yards per (dollar per yard).
As the price of the fabric increases past $425/yard, the amount of fabric which will be sold is increasing at a rate of 15 yards per (dollar per yard).
As the price of the fabric decreases past $425/yard, the amount of fabric which will be sold is decreasing at a rate of $10,000 per (dollar per yard).
As the price of the fabric decreases past $15/yard, the amount of fabric which will be sold is increasing at a rate of $425 per (dollar per yard).
As the price of the fabric decreases past $15/yard, the amount of fabric which will be sold is increasing at a rate of 10,000 yards per (dollar per yard).
Assuming the values in part (a), find R'(15).
R'(15) =
Interpret your answer in the context of this problem.
As the price of fabric decreases past $425/yard, the total revenue is increasing at $3625 per (dollar per yard).
As the price of fabric increases past $15/yard, the total revenue is decreasing at $425 per (dollar per yard).
As the price of fabric decreases past $15/yard, the total revenue is decreasing at $10,000 per (dollar per yard).
As the price of fabric increases past $15/yard, the total revenue is increasing at $3625 per (dollar per yard).
As the price of fabric increases past $425/yard, the total revenue is increasing at $10,000 per (dollar per yard).
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