Here is a simplification of the problem:

Take a look at this matrix

a1 = 3 | b1 = 4

_______________

a2 = 2 | b2 = 3

Let's say only a sum of 4 can be used from a1 + a2,

and only a sum of 4 can be used from b1 + b2.

(The use of this 4 is a constant:It correlates to the business rule I give in earlier email in bold)AND:

We need a1 + b1 to equal at least 4,

and a2 + b2 to equal at least 4. (It is just coincidental that 4 is the amount needed for each of these.)

I know intuitively that the following is the answer, but how do I figure that out with math?

2 | 2

_______

2 | 2

That is use 2 from a1, b1, a2 and b2.

ALSO: Last night I thought about finding the common denominator and started looking at something like this (which I wrote on my paper napkin as I was eating )

a1 = 3 | b1 = 4

_______________

a2 = 2 | b2 = 3

a1 + a2 = 5

a1 = 3 of the 5 or 3/5

a2 = 2 of the 5 or 2/5

following same logic

b1 = 4 /7

b2 = 3/7

New matrix:

3/5 | 4 /7

_______________

2/5 | 3/7

Now we can do a common denominator:

21/35 | 20 /35

_______________

14/35 | 15 /35

It's interesting... but I'm not sure where it gets us.

Thanks!

Anne