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

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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,270

Hi;

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,844

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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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,844

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

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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,270

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.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,844

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.

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

"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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,270

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.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,844

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).

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,270

Ahhhhhh! Nice neat code by the way.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,844

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

Must go now. Catcha L8r...

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,270

Okay, and thanks for stopping by.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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