Maximum and Minimum Values
This section explores the concept of determining maximum and minimum values for a given function over the feasible region identified from the system of inequalities.

Maximum Value ($M$): For a function $f(x)$ defined over an interval $I = { x : a leq x leq b }$, the maximum value is defined as $M = f(c)$, where $M geq f(x)$ for all $x in I$. This means that $M$ is the highest value attained by $f(x)$ in the interval $I$.

Minimum Value ($m$): Similarly, the minimum value of the function $f(x)$ is denoted as $m = f(d)$, where $m leq f(x)$ for all $x in I$. This represents the lowest value of $f(x)$ in the given interval.

Optimum Value: The term optimum value can refer to either the maximum or minimum value of a function, depending on the context of the problem being solved.

Feasible Region and Objective Function: In linear programming, the feasible region is the set of all points that satisfy all constraints (inequalities) of the problem. The objective function is the function that we want to optimize (either maximize or minimize) over the feasible region. Each vertex (corner point) of the feasible region is evaluated to determine the optimum solution.