Question

In the case of solution of a two-variable linear programming problem by graphical method, if one constraint line comes parallel to the objective function line, the problem will have:

• A. Infeasible solution
• B. Unbounded solution
• C. Degenerate solution
• D. Infinite number of solutions

Hint:

When the constraint line is parallel to the objective function, the problem has infinite solutions along the line.

Answer 1

The Correct Option is D

Step 1: Understand the graphical method.
In linear programming, when the feasible region is plotted, each constraint forms a line. The objective function is also represented as a line, and its position relative to the feasible region determines the optimal solution.
Step 2: What happens when constraint line is parallel.
If a constraint line is parallel to the objective function line, it indicates that there are multiple optimal solutions along this line. Hence, there will be an infinite number of solutions that provide the same optimal value for the objective function.