Linear Programmig Problem

Step 1: Analyze Assertion (A)
From the graph, the line passes through two corner points and , providing the same maximum value. This indicates that the maximum value occurs at infinite points along this segment. Thus, Assertion (A) is true.
Step 2: Analyze Reason (R)
In general, the optimal solution of an LPP occurs at corner points of the feasible region. This is true; however, in this case, the solution lies along a line segment connecting two corner points. Thus, Reason (R) is not the correct explanation of Assertion (A).
Step 3: Conclusion
Both Assertion (A) and Reason (R) are true, but Reason (R) does not explain Assertion (A). Hence, the correct answer is option (B).

Step 1: Plot the constraints
Graph the constraints on the Cartesian plane. The feasible region is the shaded region bounded by these lines.
Step 2: Find corner points
The corner points of the feasible region are:
Step 3: Evaluate at each point

Conclusion: The maximum value of is , which occurs at .