Help me, plz!!!!!!

[penny_love]

A rectangular box has volume 324 cubic cms and a square base of edge length x cms. The material for the base of the box costs 2 cents per square cm and the material for the top and sides costs 1 cent per square cm.
-Express the total cót C of the box as a function of x.
-What value of will minimize the costs function C???


Many thanks!!!!:wavey:

[Dark Angel]

To illustrate the given information, I drew this picture. Did I get right information?


http://i112.photobucket.com/albums/n175/SilentDude/rectangularbox.jpg

[penny_love]

Thank you very much!!!
Are you very good at maths????

[Dark Angel]

No! It's too... soon to say thanks to me! >.< The problem is still not finished!
The answer for the 1st question must be a function of x. It means that's just an expression with the variant X and some constants which we may reduce from the information I showed in the picture! ^^
And the answer for the second question is that we have to prove some element that if it was influenced, the value of the function we found from question 1 would be changed so and may reach to the minimum value. ^^
Nothing is solved yet! Let's try ^^

[Sunshine*]

I havent have math for almost a year, and I dont have it this semester. I'm soo lost by just looking at the diagram and the question :|

[Mua Sao Bang]

I'm confused of what kind of value ?

[penny_love]

I think X should equal A because it is a square base of edge length X cms. At that time area of each square base and top of the box is X*X. The area of each side is B*X.
-The costs for the base of the box: 2*X*X (cents)= 2X'' Note: 2X'' = 2X binh phương
-The costs for the top of the box: 1*X*X (cents)=X''
-The for four sides of the box: 4*B*X (cents)= 4BX
=> The costs for box: C= 2X" + X" + 4BX = 3X" + 4BX.(1)
In addition, the volume of box is 324 cubic cms
<=> V= B*X*X= B*X" = 324 => B= 324/X" (2)
(1) & (2) => C= 3X" + 4*324/X"*X
<=> C= 3X" + 1296/X

Do you think so??????

[Dark Angel]

Yea! I missed that information! I didnt think it's a square! yay! A=X Its finished >.<

@Hoa Phượng Đỏ::: well, just follow the given informaton step by step and you may see solutions to solve the problem. :)

[Sunshine*]

Well, the problem is already solved :hihi::hihi: I'm not good with this type of math :|

[penny_love]

thanks everybody!!!
However, the second question actually drives me nuts!!!!!

thanks everybody!!!
However, the second question actually drives me nuts!!!!!

[Dark Angel]

thanks everybody!!!
However, the second question actually drives me nuts!!!!!


Oh my... its so obvious!!! From the expression you got above C= 3X" + 1296/X, C is completely depend on X, isn't it. ^^ The value range of X is (0,+infinity) (because X is the length so it can NOT be smaller or EQUAL 0, X can NOT be 0 because it's the denominator in the expression C, moreover, it's the length of the box. How can 0 be a value of a length??:so_funny: So, If X is minimized then C will be minimized too! That's it! :wavey:

[Mua Sao Bang]

it should be (0 to infinitive). Oh, my god. I'm taking calculus, but the questions in this problem makes me confused. You guys are right! now, it was solved

[phongdeptrai]

Please!You are write vietnammese.You are bad english ,dont write.I live girl, if you are girl ,at [email protected]

[Dark Angel]

it should be (0 to infinitive) (infinitive: adjective! we call it's "ìnfinity". bcz you asked me to correct you :fi: ). Oh, my god. I'm taking calculus, but the questions in this problem makes me confused. You guys are right! now, it was solved

I dont think we need to take calculus, just do this: limC(x) (x=0 to infinity) for the second question I think. But the result was so clear!




Please!You are write vietnammese.You are bad english ,dont write.I live girl, if you are girl ,at [email protected]

What's going on guy??? :thatall: something funny after solving a headache problem???:so_funny:

[Mua Sao Bang]

Dark Angle :I dont think we need to take calculus, just do this: limC(x) (x=0 to infinity) for the second question I think. But the result was so clear!

Dark, infinitive is a noun. "_"

[Dark Angel]

Dark, infinitive is a noun. "_"

Oops, my bad! hehe I checked it already. Yea, "infinitive" is a noun. I thought its a adjective bcz its ended by "...ive" >.< Ok, thanks for reminding me :) but I saw ppl use "infinity" to talk about the limitation of number in math :)

[penny_love]

Yeah!!!! Infinitive is a noun but I agree that infinity is used in maths not infinitive

[Mua Sao Bang]

Uhm, I think I was wrong. Let me check again!

[^^ZhiXiang^^]

well for this one, calculus is the easiest solution.
Figure out the function then just an easy step of Derivative and you'll get it. ^^
May I ask first, the 2nd question asking for the value of what?? is it X?
Either way, to minimize the cost we have to minimize the area of the box, yet keep the same volume.
By the way, in the picture of Dark Angel i'm not agree with the small sides and the big sides he point out, since the base is a square with each side = x, then we will have a base and top with the same area, and the 4 sides have equal area.
For my answer I would say:
I dont have time to draw a picture now but, imagine one rectangular box with square base and top, and 4 sides have the same area.
B= base area = top area, S= side area, x = side of the base, h = height of the box, C = cost
Taken from the info:
C = 2B + 1B + 4S ==> C = 3B + 4S = 3x^2 + 4(x*h).
V = x^2 * h = 324
==> h = 324/x^2
C = 3x^2 + 4(324/x) =======>>>>>>> first answer yay!!!
second answer:
take the derivative of C in term of X.
C' = 6x - 4(324/x^2)
Find x where the 1st derivative = 0
6x - 1296/x^2 = 0
6x^3 - 1296 = 0
x^3 = 1296/6
x^3= 216 =>>> x = 6
use 2nd derivative test we have:
C'' = 6 + 2592/x^3. at x = 6 C''= 6+ 2592/6^3 > 0 (this one is pretty obvious)
============>>>>>>> at x = 6 C is minimum. by 2nd derivative test.
now there is x you can get anything else you want.
Good luck !!! ^^

by XiangXiang

[^^ZhiXiang^^]

Dark Angel: your answer is wrong just because a small mistake ^^, the problem says: square base with a side of x so where did that A come from ^^:rain: The problem is really easy

[Dark Angel]

hehe please read the 7th and 8th post...

and the numbers in the picture were not the answers yet! Thats just a synopsis. Dont be hasty with your answer... take a review carefully

[^^ZhiXiang^^]

oopss sorry, i didnt read those comment. well.
the 2nd answer for the problem, x = 6.
Take a look at the function it's a positive quadratic, so there must be a minimum with X can NOT be 0.
I'm not agree with when X is minimized C is also minimized for all X from 0 to infinity.
mainly because of the part 1296/x.