Question

Define feasible region.

Answer 1

Hint: It is related to the chapter linear programming and used in the topic mathematical optimization by using the given constraints. Now, define it.

Complete step-by-step answer:

A feasible region is defined as an area bounded by a set or collection of coordinates that satisfy a system of given inequalities.
The region satisfies all restrictions imposed by a linear programming scenario.
It is a concept of an optimization technique. It means a feasible region is the set of all points whose coordinates satisfy the constraints of a problem.
Explanation:-
For example, for constraints
$\begin{align}
  & x\ge 0, \\
 & y\ge 0 \\
 & x+y\le 6 \\
 & y\le x+3 \\
\end{align}$
The feasible region is shown below which is represented by an area bounded by all above equations.

The area represented above is termed as a feasible region.
Hence, a planner can use linear programming to determine the best value obtainable under conditions dictated by several linear equations that relate to a real-life problem. So, In mathematics optimization , a feasible region is the set of all possible points of an optimization problem that satisfy problems constraints , potentially including inequalities , equalities and integer constraints.

Note: One can get confused with the similar term i.e. feasible region in mathematical optimization.
If the constraints of an optimization problem are mutually contradictory, there are no points that satisfy all the constraints and thus a feasible region has null set. In the above problem, it has a solution and is said to be feasible.