• Welcome! The new FreeMathHelp.com forum is live. We've moved from VB4 to Xenforo 2.1 as our underlying software. Hopefully you find the upgrade to be a positive change. Please feel free to reach out as issues arise -- things will be a little different, and minor issues will no doubt crop up.

Practical use of max/min values, implicit differentiation.

Rich131

New member
Joined
Mar 12, 2013
Messages
4
Hi guys, this is my first post here. I will hopefully be able to help others but at the moment I have run into a problem where I don't really know where to start. I'll just get on with posting the question.

In a production process, the total production cost per day is given by the function

P = 1500x - x[SUP]2[SUB] - [/SUB][/SUP]25y/x

where x is the total number of items produced per day and y is the number of
production line workers.

On a day where each production line worker produces 25 items each, find the number
of items produced (value of x) that maximises the production cost that day.

Now what I understand of this is that I should differentiate with respect to x, but I have been trying to do implicit differentiation with no success. I used the quotient rule to solve -25y/x but my answer differs from that on WolfraamAlpha.

Any help would be greatly appreciated, specifically an explanation and direction of where to go once I have dy/dx.
Thanks in advance!
 

Rich131

New member
Joined
Mar 12, 2013
Messages
4
Unfortunately I do not have a boss. This question comes from a management science module in a course in Management of IT/IS. I have not come across partial differentiation nor is it in the book prescribed to the module. Is it required to complete the question?
 

JeffM

Elite Member
Joined
Sep 14, 2012
Messages
3,174
Hi guys, this is my first post here. I will hopefully be able to help others but at the moment I have run into a problem where I don't really know where to start. I'll just get on with posting the question.

In a production process, the total production cost per day is given by the function

P = 1500x - x[SUP]2[SUB] - [/SUB][/SUP]25y/x

where x is the total number of items produced per day and y is the number of
production line workers.

On a day where each production line worker produces 25 items each, find the number
of items produced (value of x) that maximises the production cost that day.

Now what I understand of this is that I should differentiate with respect to x, but I have been trying to do implicit differentiation with no success. I used the quotient rule to solve -25y/x but my answer differs from that on WolfraamAlpha.

Any help would be greatly appreciated, specifically an explanation and direction of where to go once I have dy/dx.
Thanks in advance!
Have you given the problem exactly? Does it say anything about implicit differentiation?

It is given that \(\displaystyle \dfrac{x}{y} = 25.\)

If your cost function is \(\displaystyle p = 1500x - x^2 - 25\left(\dfrac{y}{x}\right),\)

\(\displaystyle then\ p =1500x - x^2 - 25\left(\dfrac{1}{\frac{x}{y}}\right) = 1500x - x^2 - 25\left(\dfrac{1}{25}\right) = 1500x - x^2 - 1.\)

Now differentiate p with respect to x.

I deleted my first post. No, you do not need to do partial differentiation because x / y is given.
 
Last edited:

Rich131

New member
Joined
Mar 12, 2013
Messages
4
Thank you!

I don't know how I missed x/y being given to me in the question. I assumed (foolishly) that I would have to implicitly differentiate as the questions were getting progressively more difficult and the one before it was implicit.

So all I have to do now is differentiate

1500x - x[SUP]2[/SUP] - 1


and let it = 0 to get x?

Also, how do you get the math style text? Thanks again Jeff!
 

JeffM

Elite Member
Joined
Sep 14, 2012
Messages
3,174
I don't know how I missed x/y being given to me in the question. I assumed (foolishly) that I would have to implicitly differentiate as the questions were getting progressively more difficult and the one before it was implicit.

So all I have to do now is differentiate

1500x - x[SUP]2[/SUP] - 1


and let it = 0 to get x? Yes

Also, how do you get the math style text? Thanks again Jeff!
Well I missed it too, but before I could delete my post to correct myself, you had already responded.

If you click on my original post, you will see the coding required to get some math style text. Unless you are going to ask a lot of questions, it probably is not worth your time to learn LaTeX coding though the tutors will be grateful if you do.
 

Rich131

New member
Joined
Mar 12, 2013
Messages
4
\[ \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\]


Yeah that took longer than I expected, main issue was I wrapped it in CODE tags.. I suppose it's relatively useful to know right?
 

JeffM

Elite Member
Joined
Sep 14, 2012
Messages
3,174
Top