Linear Programming - How to maximise the maximum I want to do the following:
max: greatest(a1+b1+c1, a2+b2+c2, a3+b3+c3);
... constraints involving a1,a2,a3,b1,b2,b3,c1,c2,c3...

Since there is no greatest() function, I restructured it like this:
max: greatest_val;
greatest_val >= a1+b1+c1;
greatest_val >= a2+b2+c2;
greatest_val >= a3+b3+c3;
... constraints involving a1,a2,a3,b1,b2,b3,c1,c2,c3...

But this leads to a boundless problem as greatest_val can go to infinity.
How do I structure this problem so that it has upper and lower bounds??
Thanks in advance.

It may seem strange, but you should try to minimise greatest_val. This will give you the smallest of the possible maxima. It is sometimes called a minimax problem.
