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finding maximum/minimum of a function subject to varying inputs, please help!

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Dear all
I have the following need to be solved in matlab for my project.
I have 24 time series fitted by AR(1) model. 12 of them are combined into 1 time series X, another 12 are combined into another time series Y. There are 24 different weights for the 24 time series.
X = (a1*X1 + a2*X2 + ... + a12*X12)/(a1+...+a12) a1...a12 are weights
Y = [(b1*Y1)*(b2*Y2)* ... *(b12*Y12)]^(1/12) b1...b12 are weights
I want to find the following:
Maximum/minumum of (X-Y) by varying the weights from a1 to b12.
Each weight has a constrain as positive integer from 1 to a fixed number.
Many thanks!

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