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Default Solving equations programmatically

I need to solve a business problem which can be expressed as

Ax + By +Cz = T

where I need to find A, B and

x, y and z are constant (for the duration of the equation) and know
A, B and C are subject to a constraint such that A, B and C must not exceed a given percentage of (A+B+C

I need to be able to roll a solution across several columns (representing months of the year) in a worksheet - any ideas on how to do it

The business problem behind this is..

1. Need to generate a certain level of income from 3 types (A, B & C) of resource (call this level Target or T
2. Resources generate income at a rate of x, y and z per mont
3. Must be able to specify the resource mix - eg 60% of total resources must be A, 25% B and 15%
4. what (for any given value of T) is the correct resource mix? ie what are the values of A, B and

any help greatly value

thank

Simon
 
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