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# Optimization of single value

Hi. I have not built models in SAS before, but any help would be greatly appreciated. Ultimately, I would like to find the optimal "score" values in the following table:
age_LB | age_UB | score
20 | 29 | 20
30 | 39 | 30
40 | 49 | 40

A score gets assigned depending on the age of the person according to the values above. The dataset would look something like this:
name | age | GB | Score
peter | 21 | G | 20
jo | 31 | G | 30
mary | 41 | G | 40
sam | 21 | B | 20
paul | 31 | B | 30
jane | 41 | B | 40

Now what I need to do is to change the scores in the first table such that the following statistic is maximized:
(Mean_G - Mean_B)^2/(0.5*(Variance_G^2 + Variance_B^2))
where Mean_G is the mean score for the "G"'s, etc.

Also, there is also a criterion that the scores must not decrease as the age increases and they cannot be negative (e.g. the scores must go 20 < 30 < 40).

Any ideas on how to go about tackling this problem? Thanks very much!
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