Question

The common region determined by all the constraints of a linear programming problem is called:

• A. an unbounded region
• B. an optimal region
• C. a bounded region
• D. a feasible region

Hint:

In linear programming, the feasible region consists of all points that satisfy the system of inequalities, representing the possible solutions to the problem.

Answer 1

The Correct Option is D

Step 1: Understanding the feasible region.
In a linear programming problem, the feasible region is defined as the set of all points that satisfy the system of inequalities. It represents all potential solutions that meet the given constraints. Step 2: Evaluate the options.
- (A) Unbounded region: This can occur depending on the nature of the constraints, but it is not always the case. - (B) Optimal region: Refers to the best solution within the feasible region, not the region itself. - (C) Bounded region: The feasible region could be bounded, but it is not necessarily so in every scenario. - (D) Feasible region: This is the region that is formed by the constraints, which is always the common area where all inequalities overlap. Step 3: Conclusion.
Thus, the correct answer is: \[ \boxed{\text{Feasible region}}. \]