Question

A manufacturer produces bolts of a fabric with a fixed width. Thequantity q of this fabric (measured in yards) that is sold is afunction of the selling price p (in dollars per yard), so we canwrite q= f(p). Then the total revenue earned with selling price pis R(p)= pf(p).

a. What does it mean to say that f(20)= 10,000 and f firstderivative (20)= -350?
b. Assuming the values in part a, find R first derivative (20) andinterpret the answer.

Answer 1

3000

Explanation:

Given that 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 canwrite q= f(p). Then the total revenue earned with selling price pis R(p)= pf(p).

a) f(20) = 10000 and f'(20) = -350 means

when price is 20 dollars, sales units are 10000 units.

And when price is increased by 1 dollar, i.e. 21 sales would decrease by 350 i.e. 9650

b) To find R'(20)

`R(p) = pf(p)`

Use product rule for differentiation

`R'(p) = p f'(p) +1 f(p)`

Substitute p =20

`R'(20) = 20f'(20)+1f(20)\\R'(20) = 20(-350)+10000 = 3000`