A manufacturer produces bolts of a fabric with a fixed width. The quantity q of this fabric (measured in meters) that is sold is a function of the selling price p (in dollars per meter), 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 O There are 325 total m of fabric and $20 to spend on it. O When the price of fabric is $20/m, 325 m will be sold. O When the price of fabric is $20/m, 10,000 m will be sold. O There are 10,000 total m of fabric and $325 to spend on it. O When the price of fabric is $325/m, 20 m will be sold. What does it mean to say that f'(20) = -325? O As the price of the fabric increases past $325/m, the amount of fabric which will be sold is increasing at a rate of 20 m per (dollar per meter). O As the price of the fabric increases past $20/m, the amount of fabric which will be sold is decreasing at a rate of 325 m per (dollar per meter). O As the price of the fabric decreases past $325/m, the amount of fabric which will be sold is decreasing at a rate of $10,000 per (dollar per meter). O As the price of the fabric decreases past $20/m, the amount of fabric which will be sold is increasing at a rate of $325 per (dollar per meter). O As the price of the fabric decreases past $20/m, the amount of fabric which will be sold is increasing at a rate of 10,000 m per (dollar per meter). (b) Assuming the values in part (a), find R'(20). R'(20) = Interpret your answer. As the price of fabric increases past $ /m, the total revenue is ---Select-- v at $ per (dollar per meter).

Question
A manufacturer produces bolts of a fabric with a fixed width. The quantity q of this fabric (measured in meters) that is sold is a function of the selling price p (in dollars per meter), 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
O There are 325 total m of fabric and $20 to spend on it.
O When the price of fabric is $20/m, 325 m will be sold.
O When the price of fabric is $20/m, 10,000 m will be sold.
O There are 10,000 total m of fabric and $325 to spend on it.
O When the price of fabric is $325/m, 20 m will be sold.
What does it mean to say that f'(20) = -325?
O As the price of the fabric increases past $325/m, the amount of fabric which will be sold is increasing at a rate of 20 m per (dollar per meter).
O As the price of the fabric increases past $20/m, the amount of fabric which will be sold is decreasing at a rate of 325 m per (dollar per meter).
O As the price of the fabric decreases past $325/m, the amount of fabric which will be sold is decreasing at a rate of $10,000 per (dollar per meter).
O As the price of the fabric decreases past $20/m, the amount of fabric which will be sold is increasing at a rate of $325 per (dollar per meter).
O As the price of the fabric decreases past $20/m, the amount of fabric which will be sold is increasing at a rate of 10,000 m per (dollar per meter).
(b) Assuming the values in part (a), find R'(20).
R'(20) =
Interpret your answer.
As the price of fabric increases past $
/m, the total revenue is ---Select-- v at $
per (dollar per meter).
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Transcribed Image Text

A manufacturer produces bolts of a fabric with a fixed width. The quantity q of this fabric (measured in meters) that is sold is a function of the selling price p (in dollars per meter), 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 O There are 325 total m of fabric and $20 to spend on it. O When the price of fabric is $20/m, 325 m will be sold. O When the price of fabric is $20/m, 10,000 m will be sold. O There are 10,000 total m of fabric and $325 to spend on it. O When the price of fabric is $325/m, 20 m will be sold. What does it mean to say that f'(20) = -325? O As the price of the fabric increases past $325/m, the amount of fabric which will be sold is increasing at a rate of 20 m per (dollar per meter). O As the price of the fabric increases past $20/m, the amount of fabric which will be sold is decreasing at a rate of 325 m per (dollar per meter). O As the price of the fabric decreases past $325/m, the amount of fabric which will be sold is decreasing at a rate of $10,000 per (dollar per meter). O As the price of the fabric decreases past $20/m, the amount of fabric which will be sold is increasing at a rate of $325 per (dollar per meter). O As the price of the fabric decreases past $20/m, the amount of fabric which will be sold is increasing at a rate of 10,000 m per (dollar per meter). (b) Assuming the values in part (a), find R'(20). R'(20) = Interpret your answer. As the price of fabric increases past $ /m, the total revenue is ---Select-- v at $ per (dollar per meter).

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