Inventory Management: Find change in cost, given cost fcn...

[AGlas9837]

I have another (derivative) word problem I could use some help with: The annual inventory cost for a manufacturer is given by C = 1,008,000/Q + 6.3Q where Q is the order size when the inventory is replenished. Find the change in annual cost when Q is increased from 350 to 351, and compare this with the instantaneous rate of change when Q = 350.

For the change in annual cost, I substituted 350 and 351 into the original equation giving:

C = 1,008,000/(350) + 6.3(350) = 5085
C = 1,008,000/(351) + 6.3(351) = 5083.1

To get the instantaneous rate, I know I need the derivative but I'm not sure how to get. It doesn't look like the quotient rule would work (if I'm wrong, is 6.3Q part of the numerator?). How do I get?

 

[tkhunny]

This is exactly the same problem. It is very revealing. You simply MUST upgrade your elementary calculus. You will not survive this course without a decent review.

You do not need the quotient rule, though it would work if you could do it with sufficient care.

\(\displaystyle C(Q)\;=\;\frac{1,008,000}{Q} + 6.3Q\;=\;1,008,000Q^{-1} + 6.3Q\)

\(\displaystyle \frac{dC}{dQ}\;=\;(-1)(1,008,000)Q^{-2} + 6.3\)

 

[AGlas9837]

Thank you. I'm not sure what you mean by elementary calculus though. I only took precalculus as a prerequisite for this course and we didn't do anything even remotely similar to what I'm doing now. At any rate, after my next test I may reconsider continuing this class because tutoring is almost nonexistent at my school.

 

[tkhunny]

Fine, then, without calculus, your book or instructor MUST have given you some way to find the "instantaneous rate of change". You can't do it without that.

You used the words "derivative" and "quotient rule". No one told you this is calculus? Well, you made it!! You've done some calculus. There is not end to what you can learn, now.