Optimization is the branch of mathematics that deals with the analysis and modeling of the constraints of a given problem, in order to find the solution that maximizes or minimizes the function to be optimized.
The function to be optimized corresponds to the desired objective while taking into account the variables of the given problem. For example, one might want to minimize expenses, maximize profits, minimize production time, etc.
A constraint is a limit that is imposed on a quantity, represented by a variable. We express a constraint as an inequality which can be represented graphically in a Cartesian plane by a boundary line dividing the plane. After drawing all the constraints of a problem, the polygon of constraints is obtained.
The concept sheets in this section are primarily dedicated to inequalities. We will present the different ways to express them, such as with a number line, with set-builder notation or in tabular-form. Then, the main interest will become how to represent inequalities in a Cartesian plane and solve them algebraically. Finally, the last concept sheets will discuss systems of inequalities and methods for solving optimization problems.
