A standard linear maximisation problem is a problem of the form:

Maximise an objective function z(x1, x2, … xn), subject to the values of the variables all being nonnegative and the m constraints f1(x1, x2, … xn) ≤ a1, f2(x1, x2, … xn) ≤ a2, fm(x1, x2, … xn) ≤ am all being satisfied, where the functions z and fi are all linear combinations of their parameters with nonnegative coefficients.

The constraints describe a feasible region; the problem, then, is to find the point within the feasible region which gives a value for z no less than any other point in the region.