The first two constraints, x1 ≥ 0 and x2 ≥ 0 are called nonnegativity constraints. The other constraints are then called the main constraints. The function to be maximized (or minimized) is called the objective function. Here, the objective function is x1 + x2.
Two classes of problems, called here the standard maximum problem and the standard minimum problem, play a special role. In these problems, all variables are constrained to be nonnegative, and all main constraints are inequalities.
That post spurred me on to look up LINGO and see that it’s actually still around.