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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: 100,364

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: 100,364

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.** **Thinking is cheating.**

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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: 100,364

Did you install the latest JRE?

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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: 100,364

What are you running?

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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: 100,364

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: 100,364

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

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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: 100,364

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

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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: 100,364

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.

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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: 100,364

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.

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 15,955

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: 100,364

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.

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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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