ABSTRACT
The field of operations research uses mathematics and statistics to examine any problems that may arise where operations take place, such as in a manufacturing environment. In general, the managers of these environments have two primary fiscal goals: minimizing costs and maximizing profits. To put it differently, a rational entrepreneur should constantly look for ways to deploy finite resources in the most efficient manner while creating products or services.
Optimization theory is a branch of mathematics dealing with the critical values of functions, such as optimum, extremum, or saddle points or values. Cost minimization and profit maximization are common goals of linear programming, which is an optimization technique often employed in the business world for a broad variety of planning challenges. A linear programme has solely linear functions and constraints of this model often relate to the available resources of a company. For instance, a linear optimization model may be developed to figure out the ideal mix of production levels for each product to maximize total profit or reduce total cost.
Mathematical models of cost reduction and profit maximization are not just opposites or reciprocals of each other, and a planner must develop distinct models for each sort of optimization issue. Furthermore, optimization problems arise not only in operations planning but also in the field of economics.
This chapter explains how to convert a manufacturing case into the language of mathematics by describing formal connections between decision variables as a linear optimization model, as well as how to code and solve this translated problem using the R programming language.
