Calculus 1

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Hira Javaid

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Naomi is a business major who invented a remote control that transforms bad professors into good ones. She is currently selling 2000 remotes per month to students at a price of $10 each.
(a) How much revenue is she currently making per month?
Naomi believes she can make a larger profit by increasing the price on each remote.
(b) If the price per remote becomes $10 + x, how much revenue will Naomi now be making per month? Write an expression involving x.
As the price per remotes go up, fewer students can afford the cost. Students start to opt out of buying one.
(c) If the number of students buying remotes per month is 2000 − 20x, how much revenue is Naomi now making per month? Write an expression involving x.
(d) Naomi decides to use her knowledge of calculus to make more money. How much more than $10 should she sell each remote for to maximize her revenue?


Solution:
I need to confirm first three parts and need help in proceeding last part.

a) Revenue=10×2000=20000

b) revenue=(10+x)(2000)

c)revenue=(2000-20x)/10

Am i solving these parts right or not kindly please help.
thanks
 
Hira Javaid said:
I need to confirm first three parts and need help in proceeding last part.

a) Revenue=10×2000=20000

b) revenue=(10+x)(2000)

c)revenue=(2000-20x)/10
Click to expand...
Can you explain your thinking for part (c)? Once that's right, we can move on to (d).
 
I think in part c expressiom for number of students is given and we know that she sells a remote for $10, and we need to find the revenue she is making per month. So wrote the expression for this as (2000-20x)/10 but now i think it should be (2000-20x)(10) may be to get the revenue. I don't know exactly, i am confused
 
So i got to know that the actual revenue for part c will be (2000-20x)(10+x).
For part d i think i would need to find x..am i right?
 
Hira Javaid said:
So i got to know that the actual revenue for part c will be (2000-20x)(10+x).
For part d i think i would need to find x..am i right?
Click to expand...
Hira Javaid said:
(d) Naomi decides to use her knowledge of calculus to make more money. How much more than $10 should she sell each remote for to maximize her revenue?
Click to expand...
Yes, it will be a value of x; do you know how to maximize an expression like this? (You actually don't need calculus, but you were told to do so.)
 
I think it would take a week to get to know about the solution i am sorry(just saying it because of so much delay in comment approval)
 
Hira Javaid said:
I think we need to differentiate it to get maximum value...and then find x
Click to expand...
Just do it! You don't need to wait for approval before continuing.

What do you get when you differentiate y = (2000-20x)(10+x)? You may want to expand the expression first.

Hira Javaid said:
I think it would take a week to get to know about the solution i am sorry(just saying it because of so much delay in comment approval)
Click to expand...
You should no longer have the delay:

I'm new. Why doesn't my post appear?

This forum takes a proactive approach to prevent SPAM. Posts submitted by new members are placed in a queue, to be checked by a moderator. That means all new members must wait for their initial posts to be approved. After a post is approved, it will appear on the board. The approval process...
www.freemathhelp.com
 
Hira Javaid said:
I think it would take a week to get to know about the solution i am sorry(just saying it because of so much delay in comment approval)
Click to expand...
You got very useful response (direction) within ~24 hrs. You posted your problem in a "free" website supported by VOLUNTEER tutors - from half-way-around the world (with ~12 hr. time difference). So when you are waiting for "free" response - we are sleeping here.

If you want more timely response - you should probably check into multiple "paid" math-sites that are available (or may be a private tutor).
 
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