Thread: Interesting Algebra Problem: Predicting Qualification

Hi,

I am a computer programmer and work for a multi-level marketing company and am creating an application that will help Sellers to predict whether they will promote to the next level.

I have been stuck on the following problem, and am hoping some algebra-wizzes out there can assist me.

Here is a real example of what has happened to a Seller in the past.

BUSINESS RULE: A Seller can only use a total of 128000 maximum points from each DownLine over the 3 month qualification period.

Note: This Seller has 2 Downlines, so 12800 x 2 = 24800 points total can be used over 3 months. There are enough points available, the trick is to determine how many points from each Downline to use each month so that the maximum points rule (above) for each Downline is not broken. Even if glancing at this, you can tell me the answer, what I need is an algebraic formula that I can use with different numbers for different Sellers to derive the answer. For instance: I know intuitively, the following (which is the second bold group near the bottom of this email), but I want to be able to derive it via an algorithm:
Month2TotalDownline1PointsUsedToReachNEEDED: 0
Month2TotalDownline2PointsUsedToReachNEEDED: 0

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MaxPointsOver3MonthsUsableFromADowline: 128000

Month1PointsNEEDED: 110360
Month2PointsNEEDED: 0
Month3PointsNEEDED: 113320

Month1TotalDownLine1Points: 105234
Month1TotalDownLine2Points: 50306.50

Month1TotalAllLegsPoints: 155540.50

Month2TotalDownLine1Points: 99591
Month2TotalDownLine2Points: 45985
Month2TotalAllLegsPoints: 145567

Month3TotalDownLine1Points: 99591
Month3TotalDownLine2Points: 45985
Month3TotalAllLegsPoints: 145567


Month1TotalDownline1PointsUsedToReachNEEDED: ???? // total Month1 = 110360
Month1TotalDownline2PointsUsedToReachNEEDED: ???? // total Month1 = 110360

Month2TotalDownline1PointsUsedToReachNEEDED: ???? // total Month1 = 0
Month2TotalDownline2PointsUsedToReachNEEDED: ???? // total Month1 = 0

Month3TotalDownline1PointsUsedToReachNEEDED: ???? // total Month1 = 113320
Month3TotalDownline2PointsUsedToReachNEEDED: ???? // total Month1 = 113320


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Thank you so much for whatever help any of you are able to give me to assist me in solving this problem and improving my algebra so I am better able to solve problems like this and assist others with them in the future!

Anne

PS. Please let me know if I should be posting this in a different forum.

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