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adoni [48]
3 years ago
10

A manufacturer produces bolts of a fabric with a fixed width. A 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).
Find R′(20), given f(20)=13000 and f′(20)=−550. Also explain, what these equations mean.
Mathematics
1 answer:
BigorU [14]3 years ago
7 0

Answer:

R'(20) = 2000

Step-by-step explanation:

We are given the following in the question:

Quantity, q

Selling price in dollars per yard, p

q=f(p)

Total revenue earned =

R(p)=pf(p)

f(20)=13000

This means that 13000 yards of fabric is sold when the selling price is 20 dollars per yard.

f′(20)=−550

This means that increasing the selling price by 1 dollar per yards there is a decrease in fabric sales by 550.

We have to find R'(20)

Differentiating the above expression, we have,

R'(p) = \displaystyle\frac{d(R(p))}{dp} = \frac{d(pf(p))}{dp} = f(p) + pf'(p)

Putting the values, we get,

R'(p) = f(p) + pf'(p)\\\\R'(20) = f(20) + 20(f'(20))\\\\R'(20) = 13000 + 20(-550) = 2000

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