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#1 2013-01-17 12:39:06

cooljackiec
Member
Registered: 2012-12-13
Posts: 160

math

The Phony Bologna Meat Company offers two platters. Platter A comes with 4 hamburgers, 3 hot dogs, and 2 pig's feet, and costs $15. Platter B comes with 3 hamburgers, 4 hot dogs, and 5 pig's feet, and costs $12.

A picnic organizer requires 220 hamburgers, 270 hot dogs, and 250 pig's feet. (There can be leftovers, but these are the minimum requirements.) What is the minimum cost (in dollars)?


I see you have graph paper.
You must be plotting something
lol

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#2 2013-01-17 15:31:16

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,748

Re: math

Hi;


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#3 2013-01-18 00:52:08

phrontister
Real Member
From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 3,811

Re: math

Hi cooljackiec,

I couldn't think of a mathematical way of doing this, so programmed it in LibertyBASIC.

Last edited by phrontister (2013-01-18 16:02:45)


"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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#4 2013-01-19 11:13:00

phrontister
Real Member
From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 3,811

Re: math

Hi Bobby,

I didn't know how to go about this other than by examining all the possibilities with LB. What method did you use? 


"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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#5 2013-01-19 13:22:37

scientia
Member
Registered: 2009-11-13
Posts: 222

Re: math


Suppose the order is for
of Platter A and
of Platter B. Then we have:



We want to minimize

subject to the above constraints. Let us then rewrite the above inequalities in terms of
and one of
and
, say
.





The 1st and 2nd inequalities give

, the 1st and 3rd inequalities give
, and the 2nd and 3rd inequalities give
. The minimum appears to be 855 – however
would imply
, which does not satisfy the 2nd inequality. So we must instead have
. Thus the minimum cost is $870 dollars for 10 of Platter A and 60 of Platter B.

Last edited by scientia (2013-01-19 13:27:16)

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#6 2013-01-19 13:42:45

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,748

Re: math

Hi;

Interesting doing math with the flu.
Read 270 as 220 and added numbers up wrong. Particularly annoying because my method is pure genius. Not mine, but... Anyway 870 is correct.

What method did you use?

This is a linear optimization problem, sometimes called linear programming.

This is the cost function:

15 n + 12 m

subject to the constraints

4 n + 3 m >= 220

3 n + 4 m >= 270

2 n + 5 m >= 250

You can solve it with the simplex method and Geogebra makes the graphing easy, or just punch this in to M

Minimize[{15 n + 12 m, 4 n + 3 m >= 220, 3 n + 4 m >= 270, 2 n + 5 m >= 250}, {n, m}]


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#7 2013-01-19 14:03:25

phrontister
Real Member
From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 3,811

Re: math

Hi Bobby and scientia,

FWIW, here's what I did.

I don't understand your more advanced concepts, but I'm happy that I could scratch away and get the right answer. smile

That tiny M code is amazing! dizzy The right tool for the task. smile


"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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#8 2013-01-19 14:11:11

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,748

Re: math

Hi phrontister;

FWIW?

Yes, a program will solve many math problems. Nice solution up there in post #5 too.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#9 2013-01-19 14:18:41

phrontister
Real Member
From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 3,811

Re: math

FWIW = For what it's worth.

Re post #5: I looked at it but let it go because I was going cross-eyed (my fault, not scientia's).


"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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#10 2013-01-19 14:27:30

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,748

Re: math

Ahhhhhh! Nice neat code by the way.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#11 2013-01-19 14:48:35

phrontister
Real Member
From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 3,811

Re: math

Thanks...I'm happy with the code. Runs in the blink of an eye, too.

Must go now. Catcha L8r...


"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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#12 2013-01-19 14:53:16

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,748

Re: math

Okay, and thanks for stopping by.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

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