A company that manufactures wigdgets has hired a calculus student to determine the optimal number of widgets to produce each month in order to maximize profit. After a brief review, the student realizes that revenue is determined by

Question

R(n)= __3n^2___ +5
e^0.5n
Where n is the number of widgets produced per month, in hundreds, and revenue is measured in millions of dollars.

Determine the number of widgets that should be produced per month to maximize revenue.

Answer 1

R(n) =
_3n^2___ +5
e^0.5n

Sorry if its written poorly, its a fraction with a +5 after it

Answer 2

In the future you would write the fraction like this

R(n)= (3n^2)/(e^0.5n) + 5

We know that for a maximum of R(n), R ' (n) = 0
using the quotient rule:
R'(n) = (e^0.5n)(6n) - 3n^2(0.5) e^.5n)/(e^.5n)^2 + 0
= 0 for our max
e^.5n (6n - 1.5n^2) = 0
well, e^.5n can never be zero, so
6n - 1.5n^2 = 0
n(6 - 1.5n) = 0
n = 0 ----> that would give us our minimu, we don't care about that
or
n = 6/1.5 = 4

finish it up and state your conclusion