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#1 2013-09-17 03:37:05

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 18,885
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Constraints?

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?


'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'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

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#2 2013-09-17 03:41:23

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 90,658

Re: Constraints?

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.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#3 2013-09-17 03:55:03

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 18,885
Website

Re: Constraints?

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'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

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#4 2013-09-17 03:57:12

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,658

Re: Constraints?

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.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#5 2013-09-17 04:15:58

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 18,885
Website

Re: Constraints?

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'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

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#6 2013-09-17 04:19:13

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,658

Re: Constraints?

Did you install the latest JRE?


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#7 2013-09-17 04:21:57

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 18,885
Website

Re: Constraints?

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


'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'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

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#8 2013-09-17 04:22:39

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,658

Re: Constraints?

What are you running?


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#9 2013-09-17 04:26:25

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 18,885
Website

Re: Constraints?

like?

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


'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'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

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#10 2013-09-17 04:27:50

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,658

Re: Constraints?

Windows?

Yes you will plot those 4 and 1 more

x + y = 20


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

#11 2013-09-17 04:33:25

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 18,885
Website

Re: Constraints?

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 sad


'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'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

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#12 2013-09-17 04:37:21

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,658

Re: Constraints?

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

View Image: 2013-09-17_093334.gif

In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

#13 2013-09-17 04:45:36

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 18,885
Website

Re: Constraints?

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


'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'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

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#14 2013-09-17 04:46:57

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,658

Re: Constraints?

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.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

#15 2013-09-17 04:50:10

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 18,885
Website

Re: Constraints?

I do not see how.


'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'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

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#16 2013-09-17 04:51:04

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,658

Re: Constraints?

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.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

#17 2013-09-17 04:57:00

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 18,885
Website

Re: Constraints?

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

Have a nice day


'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'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

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#18 2013-09-17 05:01:48

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,658

Re: Constraints?

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.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

#19 2013-09-17 06:21:32

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,658

Re: Constraints?

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.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#20 2013-09-17 12:57:27

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 18,885
Website

Re: Constraints?

I got my Geogebra fixed.


'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'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

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#21 2013-09-17 23:01:35

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,658

Re: Constraints?

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.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

#22 2014-03-18 02:10:09

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

Re: Constraints?

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.


"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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