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

^{2 - }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!

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