Quality control of food products on the basis of discrete and analytical mathematical models

A mathematical model is a system of mathematical expressions that describe the characteristics of a modeling object and the relationships between them. The structure of the mathematical model includes the ratio reflecting the conditions that must satisfy the solution (plan) of the problem (the so-called system of constraints), as well as a function in mathematical form expressing the goal in terms of the selected optimality criterion (the so-called objective function). The search for the optimal plan from a mathematical point of view is the definition of such a set of numerical values of the unknown, satisfying the limiting conditions of the problem, in which the objective function reaches an extreme value (maximum and minimum). If the unknowns are included in the model only in the first degree, the problem relates to linear programming, otherwise, to nonlinear programming. Most of the practically important tasks of production planning can be described by means of linear mathematical models. In this article the generalized discrete analytical mathematical model of food production quality management will be considered. It is worth noting that the quality of the final product depends on a combination of different factors: sales, service, manufacturing and others.