I am developing production optimization SW.

My problem can most probably be solved with linear programming. I am in a process of making sure that the approach works. I made a few simple examples but got stuck.

This statement calculates nicely:

LinearProgramming [ {1,2,3}, {{1, 1, 0},{1, 0, 2},{0, 1, 1},{1, 1, 0}}, {{4, -1},{9, 1},{5,0},{3,0}} ]

This one was not understood by Wolfram (Wolfram|Alpha doesn't know how to interpret your input.):

LinearProgramming [ {1,2,3,4}, {{1, 1, 0,1},{1, 0, 0, 2},{0,1, 0, 1},{0,1, 1, 0}}, {{4, -1},{9, 1},{5,0},{3,0}} ]

What is wrong with the latter?

Examples are random and do not mean anything.