Question

Which one of the following represents the correct feasible region determined by the following constraints of an LPP?
$x + y \geq 10, \quad 2x + 2y \leq 25, \quad x \geq 0, \quad y \geq 0$

• A.
• B.
• C.
• D.

Answer 1

Answer: (C)

Answer 2

To solve this problem, we need to first plot the given constraints and identify the feasible region:

Constraint 1: x + y ≥ 10. This is a straight line with slope -1. The feasible region is above this line.

Constraint 2: 2x + 2y ≤ 25. Simplifying this inequality, we get x + y ≤ 12.5, which is a straight line with slope -1. The feasible region is below this line.

Constraint 3: x ≥ 0. This constraint restricts the feasible region to the right of the y-axis.

Constraint 4: y ≥ 0. This constraint restricts the feasible region to above the x-axis.

Thus, the feasible region is the intersection of the regions defined by these four constraints.

The graph that correctly represents this feasible region is shown in Option (3).