What is special about that list of Concert Technology classes recognized by an instance of IloCplex? A model consisting of instances of those classes can be transformed into a MIP or LP in the conventional form:

Maximize (or minimize) an objective function

such that LowerBounds <= Ax <= UpperBounds

for every lowerBound <= x <= upperBound

When all the variables, indicated by x, are continuous floating-point variables, a problem in this conventional form is known as a linear programming model (LP). When some variables are integer- or Boolean-valued, a problem in this form is known as a mixed integer programming model (MIP).

At first glance, it might appear that this formulation greatly restricts the kinds of problems that can be modeled in this way. However, practice has shown that an astonishing variety of problems can be represented by such a model. The book Model Building in Mathematical Programming by H.P. Williams offers a good starting point if you are interested in model-building techniques for LPs and MIPs.