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Running a google search for "java linear optimization" seems to have found a number of hits. I'm not familiar with any of the packages though, so I'm not sure if they are what you're looking for.
Likewise, a search for "linear optimization algorithm" turned up a few interesting articles such as the following in case you end up writing the algorithm yourself:
The wiki entry for Linear programming turned up a number of packages. Although most are not Java, the following has a Java package: [http://www.cs.washington.edu/research/constraints/cassowary/]
Edited by: jboeing on Sep 30, 2009 9:31 AM
Your solution is correct: it's a so called 'blending problem' and it is one of the oldest problems solved by the Simplex algorithm. When you google for "Java simplex" you'll find quite a few implementations of the revised simplex algorithm; curiously enough most implementations are applets; probably for educational purposes ...