Question

For a Linear Programming Problem (LPP), the given objective function \( Z = 3x + 2y \) is subject to constraints: \[ x + 2y \leq 10, \] \[ 3x + y \leq 15, \] \[ x, y \geq 0. \]

The correct feasible region is:

• A. ABC
• B. AOEC
• C. CED
• D. Open unbounded region BCD

Hint:

When dealing with Linear Programming Problems, graph the constraints to visualize the feasible region. The intersection of the inequalities defines the feasible region.

Answer 1

The Correct Option is B

The feasible region in a Linear Programming Problem (LPP) is the intersection of all constraint inequalities, representing the set of points satisfying every condition.
To determine this region:
- Graph each constraint on a coordinate plane: 
1. The equation \( x + 2y = 10 \) defines a straight line. 
2. The equation \( 3x + y = 15 \) defines another straight line. 
3. The inequalities \( x, y \geq 0 \) restrict the region to the first quadrant. 
- The feasible region is the bounded area enclosed by these lines that simultaneously satisfies all constraints. 
Based on the graphical representation, the feasible region is the area bounded by points \( A, O, E, C \), specifically identified as region \( AOEC \).