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(30) = 10,000? o When the price of fabric is $30/yard, 300 yards will be sold. When the price of fabric is $30/yard, 10,000 yards will be sold. There are 300 total yards of fabric and $30 to spend on it. There are 10,000 total yards of fabric and $300 to spend on it. o When the price of fabric is $300/yard, 30 yards will be sold. What does it mean to say that f (30) = -300? o As the price of the fabric increases past $30/yard, the amount of fabric which will be sold is decreasing at a rate of 300 yards per (dollar per yard). As the price of the fabric decreases past $ 300/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 $30/yard, the amount of fabric which will be sold is increasing at a rate of $300 per (dollar per yard). O As the price of the fabric increases past $300/yard, the amount of fabric which will be sold is increasing at a rate of 30 yards per (dollar per yard). O As the price of the fabric decreases past $30/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'(30). R'(30) = 1000 Interpret your answer. As the price of fabric increases past $300/yard, the total revenue is increasing at $10,000 per (dollar per yard). O As the price of fabric decreases past $30/yard, the total revenue is decreasing at $10,000 per (dollar per yard). As the price of fabric increases past $30/yard, the total revenue is increasing at $1000 per (dollar per yard). As the price of fabric decreases past $300/yard, the total revenue is increasing at $1000 per (dollar per yard). As the price of fabric increases past $30/yard, the total revenue is decreasing at $300 per (dollar per yard).
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(30) = 10,000? o When the price of fabric is $30/yard, 300 yards will be sold. When the price of fabric is $30/yard, 10,000 yards will be sold. There are 300 total yards of fabric and $30 to spend on it. There are 10,000 total yards of fabric and $300 to spend on it. o When the price of fabric is $300/yard, 30 yards will be sold. What does it mean to say that f (30) = -300? o As the price of the fabric increases past $30/yard, the amount of fabric which will be sold is decreasing at a rate of 300 yards per (dollar per yard). As the price of the fabric decreases past $ 300/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 $30/yard, the amount of fabric which will be sold is increasing at a rate of $300 per (dollar per yard). O As the price of the fabric increases past $300/yard, the amount of fabric which will be sold is increasing at a rate of 30 yards per (dollar per yard). O As the price of the fabric decreases past $30/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'(30). R'(30) = 1000 Interpret your answer. As the price of fabric increases past $300/yard, the total revenue is increasing at $10,000 per (dollar per yard). O As the price of fabric decreases past $30/yard, the total revenue is decreasing at $10,000 per (dollar per yard). As the price of fabric increases past $30/yard, the total revenue is increasing at $1000 per (dollar per yard). As the price of fabric decreases past $300/yard, the total revenue is increasing at $1000 per (dollar per yard). As the price of fabric increases past $30/yard, the total revenue is decreasing at $300 per (dollar per yard).
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
Related questions
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(30) = 10,000?
o When the price of fabric is $30/yard, 300 yards will be sold.
When the price of fabric is $30/yard, 10,000 yards will be sold.
There are 300 total yards of fabric and $30 to spend on it.
There are 10,000 total yards of fabric and $300 to spend on it.
o When the price of fabric is $300/yard, 30 yards will be sold.
What does it mean to say that f (30) = -300?
o As the price of the fabric increases past $30/yard, the amount of fabric which will be sold is decreasing at a
rate of 300 yards per (dollar per yard).
As the price of the fabric decreases past $ 300/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 $30/yard, the amount of fabric which will be sold is increasing at a
rate of $300 per (dollar per yard).
O As the price of the fabric increases past $300/yard, the amount of fabric which will be sold is increasing at a
rate of 30 yards per (dollar per yard).
O As the price of the fabric decreases past $30/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'(30).
R'(30) = 1000
Interpret your answer.
As the price of fabric increases past $300/yard, the total revenue is increasing at $10,000 per (dollar per
yard).
O As the price of fabric decreases past $30/yard, the total revenue is decreasing at $10,000 per (dollar per
yard).
As the price of fabric increases past $30/yard, the total revenue is increasing at $1000 per (dollar per yard).
As the price of fabric decreases past $300/yard, the total revenue is increasing at $1000 per (dollar per
yard).
As the price of fabric increases past $30/yard, the total revenue is decreasing at $300 per (dollar per yard).
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