# Lost on word problem

## Homework Statement

The cost associated with storing x units of a certain product is given by the function C(x) = 0.8x^2 - 12.8x + 2600 where C is measured in dollars and x in hundreds of units. What is the minimum cost ?

## The Attempt at a Solution

Umm, yea. I would attempt it but I have no idea where to start, but I will try anyways. So I was thinking it needs to be set up ( y = mx + b ) so I did and got a final result of : y = square root of 16x - 3250 OR : y = (16x - 3250)^.5

I then plotted it on a graph and figured that I need to find minimum x for some reason because y didn't make much sense as it came to be 0. So then the minimum x was about 204 on the graph when y = 0. So I was thinking that is my answer but have absolutely NO clue !! :rofl: Please help me !!

Do you have any knowledge of derivatives.Please tell me if i can help....it wud be great if i could help ...i myslef have only limited knowledge.However.....$$C(x) = 0.8x^2 - 12.8x + 2600$$ is the equation we have.Now if we take $$y=c(x)$$

and differentiate it with respect to $$x$$...i think you would get ur answer setting $$\frac {dy}{dx}=0$$

No clue, we haven't got that far into the book. So that would tell me that it wouldn't be necessary to use that. But as before, still not sure. I wish you could help, I have a couple days to get the answer before returning to school so hopefully someone will know.

Hm....i gues ud have to graph the equation y=C(x)= 0.8x^2 - 12.8x + 2600 !

And then what. lol

find the curves minima point.I mean where the slope is 0!.

Which would be 2600. Surely that's not right.

hage567
Homework Helper
No, the slope is not zero at when C(x)=2600! Look harder.

and that's one of my weaknesses. So after looking at it again harder, I am getting something like x is around 8 and y is around 2548 but still am not sure as to what my answer is. 2548 dollars ?

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Dick
Homework Helper
If you want to do this without using derivatives and without using a graph, complete the square in the expression for C(x). Ie write it in the form:

C(x)=0.8*(x-A)^2+B

(Where you have to figure out what A and B are). Then clearly the minimum is where x=A and it's value is?

Ahhhhhhhhh, that is what I am talking about. Didn't think of the standard form dealio. Thanks Dick.

So C(x) = 0.8(x-6.4)^2 + 2559.04 , so the minimum you are saying would be 6.4 or 2559.04. I am thinking you are saying it is 6.4 because I believe you take the opposite sign of A in the (). Correct ? 6.4 ?

Dick
Homework Helper
The value of x at which the minimum occurs is x=6.4. At x=6.4 the cost C(x) reaches a minimum value of 2559.04. The question asks for minimum cost. (I'm trusting you got the numbers right - I didn't check them).

Dick
Homework Helper
No. You didn't get the numbers right. Multiply your C(x) back out. Do you get back to the original???

I didn't divide the .8 into 12.8. This one comes out right :

C(x) = 0.8(x-8)^2 + 2536 and then you kinda lost me as to finding the minimum cost.

Dick
Homework Helper
The squared term is always greater than or equal to zero. So the x value where it is zero defines the minimum of C(x). C(8)=2536 is the minimum cost. That's pretty close to what you were seeing on your graph.

Excellent, thanks so much for the help Dick. I like your way a whole lot better than the graph way !!

Dick
Homework Helper
Glad you like it. Wait till you get to derivatives. You'll LOVE them.

Glad you like it. Wait till you get to derivatives. You'll LOVE them.

I lol'ed.

@OP:
Your textbook may have it listed as "completing the square", in case you were interested.