Maximize multiple linear equations simultaneously

This is probably best placed in linear algebra, but I don't know exactly where this fits, possibly statistical analysis or business math or some sort. Anyway I have a matrix that looks something like this

[ 1 1 0 5 1|A ]

[ 0 3 0 1 1|B ]

[ 4 1 1 0 1|C ]

[ 1 0 3 1 0|D ]

and the independant variables may be a, b, c, d, e if you will. What I am trying to do is maximize A, B, C, and D under the single constraint which may be a + b + c + d + e = x, x some arbitrary value assigned. I am not looking to maximize one single equation but all four equations simultaneously. I have done some searching for some kind of method to do this and have come up only with single linear equations being optimized. I do not pretend to be particularly handy with mathematics, or matrix math for that matter, but I am very interested if there is indeed a method to optimize multiple linear equations simultaneously under a single constraint. If not, I may have found a life goal!

Darren