ABSTRACT
There is various linear and non-linear optimization software, including CPLEX, GAMS and LINDO. This chapter shows that examples of reasoning for abstraction-deduction-interpretation for simple management problems of two variables. The first stage of abstraction corresponds to the verbal description of the problem. This description is reduced to algebra, which relates numbers and symbols in equations and formulas. The translation is done using a reference system of coordinate axes perpendicular to each other called “Cartesians,” in honor of Rene Descartes. Being problems of two variables, the objective function and the constraints can be represented as flat figures. Once the optimal decision has been obtained, it can usually be improved by relaxing the active constraints. Relaxing a constraint that represents the availability of a resource is equivalent to acquiring more of that resource, such as expanding plant capacity or hiring more staff. The marginal benefit of relaxing a certain constraint involves keeping the others fixed.
