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bobbym wrote:

Maximize P = 10 x + 25 y

For the constraints:

3 ≤ x ≤ 12

4 ≤ y ≤ 15

x + y ≤ 20

How do u do ths?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 107,815

Hi;

The first method taught is a graphical one. You must have a grapher handy. If not you will follow along from the diagrams I post.

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I think I have got Geogebra. What next?

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 107,815

The first constraint is really 2 constraints. We will enter them as equations.

Type x = 3 in the input bar.

**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.**

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That will create a vertical bar. I think the next step is to type x = 12, so as to confine the solution within these two.

My Geogebra does not seem to fire up. Neither are my other java apps running. What should I do?

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 107,815

Did you install the latest JRE?

**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.**

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I think I did. What is the way to check for sure?

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 107,815

What are you running?

**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.**

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like?

I think you are going to plot this four x=3; x=12; y=4; y=15. What about the last equation?

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 107,815

Windows?

Yes you will plot those 4 and 1 more

x + y = 20

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If you do not mind, please link me to an online grapher or post a screenshot.

I'll fix the Java later, I want to sleep

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 107,815

This the area that the 5 equations encloses. The 5 feasible points ( possible answers ) are A,B,C,D,E

**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.**

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But we were asked to max out 10 x + 25 y!

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 107,815

And you will. The feasible points are determined by the constraints and they determine the maximum of 10 x + 25 y

**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.**

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I do not see how.

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 107,815

Take the (x,y) coordinates of each of the 5 points and plug them into the objective function (10 x + 25 y) and tell me what you get.

**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.**

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I am too sleepy right now to solve those equations and find the cooridinates.

Have a nice day

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 107,815

Okay, it will be here when you get back. If you get your geogebra fixed I will show you how to do this faster.

See you later.

**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.**

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,018

Hi Agnishom

What you can do now is plot the line 10x+25y=a where a is a slider variable. You can move the slider around and your goal would be moving it right as much as possible, but so that the line has an intersection with bobbym's figure above.

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I got my Geogebra fixed.

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 107,815

Very good now you just have to plug in A,B,C,D and E into the objective function (10 x + 25 y) and tell me what you get.

**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.**

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Hi,

We can approximate by simulation (J again):

```
a=:3+9*?10000000#0
b=:4+11*?10000000#0
>./((10*a)+(25*b))*(20>a+b)
```

=424.953939391672

which is close to the exact answer of 425.

Brief explanation:

1) Get random uniform values in the range for x and y.

2) Get the maximum of 10x+25y among the values where x+y<=20

From the LPP:

`(3 5 12 12 3)([: >./ (10 * [) + 25 * ]) 15 15 8 4 4`

= 425

We can easily obtain the tacit definition using

`sim=: 13 : '>./((10*x)+(25*y))'`

Typing in sim gives the tacit definition. We can then use that output to build more complicated definitions.

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