Answer:
3000
Step-by-step 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)
[tex]R(p) = pf(p)[/tex]
Use product rule for differentiation
[tex]R'(p) = p f'(p) +1 f(p)[/tex]
Substitute p =20
[tex]R'(20) = 20f'(20)+1f(20)\\R'(20) = 20(-350)+10000 = 3000[/tex]
