Math Is Fun Forum
  Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

You are not logged in.

#1 2010-07-02 01:58:30

DaveRobinsonUK
Member
Registered: 2010-04-24
Posts: 123

Optimisation Problem

I have a problem that I can't seem to work out, or at least get started with.

Anyway here it is.

There is £120 to spend on a fence to enclose a garden. Fencing for 3 sides costs £2/m the other side costs £3/m.

a) Given the rectangle has dims x by y show that

b)Hence show that

c)Find the maximum area of the garden.

Don't know what it is with optimisation, I can do the normal differentiation problems and most of the optimisation problems, every now and then though.


Can feel it coming together.. Slowly but Surely smile

Offline

#2 2010-07-02 02:21:19

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

Re: Optimisation Problem

The fence costs £2 per metre for three of the sides, and £3 per metre for the other one.

<------- x --------->

----------------------   ^
|                         |   |
|                         |   y
|                         |   |
============   V

This bad drawing shows that the bottom side has fancy double-thickness, and that's why it's more expensive.

If the area has a length of x metres, then to enclose it you'll need x metres of normal fence and x metres of expensive fence. This comes to £5x altogether.

Similarly, if the area has a width of y metres, then the enclosure will need y metres of normal fence for one side, and another y metres for the other side, making the total cost £4y.

You have £120 to spend, so the equation is 5x+4y = 120.

The area A is given by xy.
To get the answer in b), just arrange the equation from a) until you can remove y from the area's expression.

You can do differentiation problems, so once you've got this far, c) shouldn't be a problem.


Why did the vector cross the road?
It wanted to be normal.

Offline

#3 2010-07-02 11:48:03

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Optimisation Problem

Hi Dave;

In case you get stuck:



In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Offline

#4 2010-07-02 15:12:59

Sarah Rebekah 13
Guest

Re: Optimisation Problem

Hi bobbym.

#5 2010-07-02 15:19:30

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Optimisation Problem

Hi Sarah


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Offline

#6 2010-07-03 06:49:18

Sarah Rebekah 13
Guest

Re: Optimisation Problem

good morning.

#7 2010-07-03 10:48:28

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Optimisation Problem

Good Afternoon now. Ready for the fourth?


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Offline

#8 2010-07-04 07:39:52

Sarah Rebekah 13
Guest

Re: Optimisation Problem

roflolroflolroflolroflolYes

#9 2010-07-04 08:14:37

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Optimisation Problem

Boom, boom, crack, sizzle, more explosions. Some kid is on fire, okay they put him out. He is unharmed!

Happy, fourth of July, Sarah!


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Offline

#10 2010-07-05 05:41:31

Sarah Rebekah 13
Guest

Re: Optimisation Problem

Happy Fourth of July to u.roflolroflolroflol

#11 2010-07-05 05:52:36

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Optimisation Problem

Hi Sarah;

Happy fifth of July! How was your holiday?


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Offline

#12 2010-07-06 01:34:09

Sarah Rebekah 13
Guest

Re: Optimisation Problem

good yours?

#13 2010-07-06 03:49:38

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Optimisation Problem

Hi Sarah;

Just the same as every other day.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Offline

#14 2010-07-06 21:51:47

DaveRobinsonUK
Member
Registered: 2010-04-24
Posts: 123

Re: Optimisation Problem

Hi Guys

Hi Bobby, thanks for the help and the links.

So busy at the moment with this prep work. Trying to get all this stuff into my head so I know it rather than having to refer to the book. At the moment I am just jumping back and forth between the chapters, not sure if that is the best way to go or not.


Can feel it coming together.. Slowly but Surely smile

Offline

#15 2010-07-06 22:34:13

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Optimisation Problem

Hi Dave;

Don't mention it. Holler when you need more!

Trying to get all this stuff into my head so I know it rather than having to refer to the book.

Never did agree with the way they make you stuff your cranium with the memorization of bits of information.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Offline

#16 2010-07-08 03:01:52

Sarah Rebekah 13
Guest

Re: Optimisation Problem

Coo,l:cool::cool::cool::cool::cool:

#17 2010-07-08 04:02:04

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Optimisation Problem

Sarah, what's happening!


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Offline

#18 2010-07-10 04:08:11

Sarah Rebekah 13
Guest

Re: Optimisation Problem

Just cooling off Had some Rain

#19 2010-07-10 04:20:10

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Optimisation Problem

It never rains in the summer here.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Offline

#20 2010-07-11 09:42:49

Sarah Rebekah 13
Guest

Re: Optimisation Problem

Really how its, like in your new home.?

#21 2010-07-11 10:09:36

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Optimisation Problem

I am in heaven. My brother moved back in here. Get this, an old GF is moving in here too. It is going to be a hot summer 120+ !


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Offline

#22 2010-07-12 03:29:26

Sarah Rebekah 13
Guest

Re: Optimisation Problem

That is nice.

#23 2010-07-12 04:32:53

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Optimisation Problem

Summers here at very hot. No rain and more sunshine than anywhere in the United States. Lots of tourists and hollywood types.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Offline

#24 2010-07-13 02:38:45

Sarah Rebekah 13
Guest

Re: Optimisation Problem

cool where im at we have some Tourists its Downtown i dont know why.

#25 2010-07-13 02:40:39

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Optimisation Problem

Morning Sarah;

The south is beautiful. Maybe they just want to look around.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Offline

Board footer

Powered by FluxBB