Must go now. Catcha L8r...

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

]]>FWIW?

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

]]>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.

]]>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}]

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

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

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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)?

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