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:

The feasible region is the set of all points satisfying the constraints in a linear programming problem.

Answer 1

The Correct Option is D

Step 1: Definition of feasible region.
The feasible region is the common region determined by all constraints (inequalities) in a linear programming problem. It represents all possible solutions. Step 2: Analyze the options.
- (A) Unbounded region: May or may not occur depending on constraints. - (B) Optimal region: Refers to the solution, not the region itself. - (C) Bounded region: A feasible region may or may not be bounded. - (D) Feasible region: Always the common region defined by constraints. Step 3: Conclusion.
The correct answer is: \[ \boxed{\text{a feasible region}}. \]