Question

**Will give MEDAL**
A telephone company finds there is a net profit of $15 per instrument if a given network has 1000 users. For every user over 1000, the profit decreases by 1 cent. What is the maximum profit the company can make per network?

Answer 1

@Hero

Answer 2

n = number of users
p = profit per user


Currently
n = 1000
p = 15
so the total profit would be
T = n*p
T = 1000*15
T = 15000


Let
x = number of additional users added
If we add on x users, then we go from n = 1000 to n = 1000+x


For each user added, we lose 1 cent ($0.01) in profit, per user, so
p = 15 - 0.01x


The new total profit T is
T = n*p
T = (1000+x)*(15-0.01x)


Your goal is to find the vertex of the new T function. That will allow you to determine the maximum profit possible.

Answer 3

Hint: I recommend expanding out `(1000+x)*(15-0.01x)` as your first step

Answer 4

I expanded that equation and got: T=15000+5x-.01x^2

Answer 5

Then i took the derivative and got: T'=5-.02x
When I set 0=5-.02x, I got x=250

Answer 6

very good

Answer 7

x = 250 will occur at the max. Plug in x = 250 to find the value of T

Answer 8

I plugged the x=250 into the original equation and got the answer of $15625. Does this sound like the correct answer?

Answer 9

yep, the max profit possible is $15625

so if you add on 250 more users, then you gain an additional $625 (15625-15000=625)

Answer 10

Thank you!!!

Answer 11

you're welcome