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**BooBooBilly** Not quite sure where to put this problem... I’ve completed Calc 2 and I'm currently enrolled in a C# software class. I’m writing this program that accomplishes a time efficiency analysis. Let me give you an example.

{

(A-D are “products”: V-Z are “sets”: Certain prodicts makes certain sets)

Product A makes 50 sets of Z, 100 sets of X and 500 sets V.

Product B makes 10 sets of Z, 50 sets of X and 200 sets of W.

Product C makes 40 sets of X and 300 sets of V.

Product D makes 100 sets of W and 25 sets of Z

It takes 300 minutes to make Product A, 250 minutes to make Product B, 100 minutes to make Product C and 150 minutes to make Product D.

}

Question: If you need 12000 sets of Z, 10400 sets of X, 7800 sets of V and 9400 sets of Z are needed; what is the shortest amount of time needed to make the complete number of sets?

This is my type of problem. A bit simplified but still accurate. I have about 15 “products” and 30 different “sets” in actuality. My problem is that I can’t seem to find a quick solution. Being that a computer is doing all the analysis, my first version of the software does a guess and check and compare. However, I’ve found that certain answers are not the shortest and certain questions exploit my poor programming and hits an eternal loop. I need a mathematical solution. Maybe matrices? Perhaps some complex cross graphing, area analysis?

Thanks