# Thread: exploring behaviour of minimums

1. ## exploring behaviour of minimums

Hey guys,

I'm a little stuck again. I'm wondering if someone would be able to point me in the general direction of how to complete this question??

Thankyou so much!

2. ## Re: exploring behaviour of minimums

It's basically the same as the last one.

Width is 2m.
Length is variable but given once n is chosen
instead of height you are given volume. calculate the height from the volume as before.
height becomes a function of $n$

Then a single strap length is $4+2h$ (I assume there is no strap lengthwise anymore)

You've got $n$ of these so $L=n(4+2h(n))$

Proceed on from there.

3. ## Re: exploring behaviour of minimums

Hi romsek,

once again I'm a little confused as that seems to be different to both of the resources I have (I may be wrong though.) Are either of these correct?

4. ## Re: exploring behaviour of minimums

Originally Posted by ifailedmaths
Hi romsek,

once again I'm a little confused as that seems to be different to both of the resources I have (I may be wrong though.) Are either of these correct?

oh I see, the length can be variable. I read it as a multiple of 1.5.

I'll take another look.

5. ## Re: exploring behaviour of minimums

Originally Posted by romsek
oh I see, the length can be variable. I read it as a multiple of 1.5.

I'll take another look.
thankyou, that'd be much appreciated.

6. ## Re: exploring behaviour of minimums

Originally Posted by ifailedmaths
thankyou, that'd be much appreciated.
$n=2$

$\dfrac 3 2 \leq x < 3$

$V = 2 x h$

$\ell = 2(2\cdot 2 + 2 h) = 8+4 h = 8 + \dfrac{4V}{2x} = 8 + \dfrac{2V}{x}$

$n=3$ is very similar and I'm sure you can figure it out.

I don't know what they mean by optimization. Are you supposed to select a length $x$ for a chosen $n$ such that $\ell$ is minimized?

7. ## Re: exploring behaviour of minimums

Originally Posted by romsek
$n=2$

$\dfrac 3 2 \leq x < 3$

$V = 2 x h$

$\ell = 2(2\cdot 2 + 2 h) = 8+4 h = 8 + \dfrac{4V}{2x} = 8 + \dfrac{2V}{x}$

$n=3$ is very similar and I'm sure you can figure it out.

I don't know what they mean by optimization. Are you supposed to select a length $x$ for a chosen $n$ such that $\ell$ is minimized?
Thankyou for explaining! And yes, I think so.