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 of a Linear Programming Problem (LPP) is determined by the intersection of the inequalities.
The feasible region is the set of points that satisfy all the constraints. 
- Plot the given constraints on a coordinate plane: 
1. \( x + 2y = 10 \) is a straight line. 
2. \( 3x + y = 15 \) is another straight line. 
3. \( x, y \geq 0 \) represents the first quadrant. 
- The feasible region will be bounded by the lines and will be the area that satisfies all these constraints. 
From the diagram, the feasible region is the region enclosed by the points \( A, O, E, C \), and the correct region is \( AOEC \).