Lost on Word Problem Homework: Min Cost of Storing Units

In summary, 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. The minimum cost is when x=6.4.
  • #1

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 !
 
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  • #2
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...[tex]C(x) = 0.8x^2 - 12.8x + 2600[/tex] is the equation we have.Now if we take [tex]y=c(x)[/tex]

and differentiate it with respect to [tex]x[/tex]...i think you would get ur answer setting [tex]\frac {dy}{dx}=0[/tex]
 
  • #3
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.
 
  • #4
Hm...i gues ud have to graph the equation y=C(x)= 0.8x^2 - 12.8x + 2600 !
 
  • #6
find the curves minima point.I mean where the slope is 0!.
 
  • #7
Which would be 2600. Surely that's not right.
 
  • #8
No, the slope is not zero at when C(x)=2600! Look harder.
 
  • #9
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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  • #10
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?
 
  • #11
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 ?
 
  • #12
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).
 
  • #13
No. You didn't get the numbers right. Multiply your C(x) back out. Do you get back to the original?
 
  • #14
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.
 
  • #15
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.
 
  • #16
Excellent, thanks so much for the help Dick. I like your way a whole lot better than the graph way !
 
  • #17
Glad you like it. Wait till you get to derivatives. You'll LOVE them.
 
  • #18
Dick said:
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.
 

1. What is the meaning of "Min Cost of Storing Units" in this word problem?

The "Min Cost of Storing Units" refers to the minimum amount of money that would need to be spent in order to store a certain number of units. In this word problem, the goal is to find the most cost-effective way to store a given number of units.

2. How is the minimum cost calculated in this word problem?

The minimum cost is calculated by considering the cost of each storage option and choosing the one with the lowest cost. This may involve comparing the cost per unit for different storage methods or taking into account any additional fees or expenses associated with each option.

3. Are there any constraints or limitations in this word problem?

Yes, there may be constraints or limitations in this word problem that affect the minimum cost calculation. For example, there may be a maximum capacity for each storage option or a limited budget that must be considered.

4. How does the number of units being stored affect the minimum cost?

The number of units being stored can have a significant impact on the minimum cost. Generally, the more units that need to be stored, the higher the cost will be. This is because larger quantities may require more storage space or a more expensive storage method.

5. Are there any other factors to consider when solving this word problem?

In addition to the cost, there may be other factors to consider when solving this word problem. These could include the accessibility of the storage options, the security of the units, and any potential risks or benefits associated with each option.

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