A manufacturer produces bolts of a fabric with a fixedwidth. The quantity of this fabric (measured in yards)that is sold is a function of the selling price (in dollarsper yard), so we can write q =f(p) . Then the totalrevenue 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 interpretyour answer.
A manufacturer produces bolts of a fabric with a fixed
width. The quantity of this fabric (measured in yards)
that is sold is a function of the selling price (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.
It is given that the quantity of the fabric sold is given by the function where p is the selling price
and q is the quantity of the fabric sold.
The quantity of fabric is measured in yards and the selling price is measured in dollars per yard. The total
revenue is given by .
Part a
We have . It is given that means that the quantity of fabric sold is the function
of the selling price p.
Thus, the expression means that the quantity of fabric sold is 10,000 yards when the
price is $20 per yard.
We have . The first derivative of the demand function tells us the change in amount of
fabric when the price is changed.
Thus, the expression means that for the change in price at dollars per yard, the
quantity of fabric sold is decreased by 350 yards.
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