Question

\(\text{The feasible region represented by the constraints } 4x + y \geq 80, \; x + 5y \geq 115, \; 3x + 2y \leq 150, \; x, y \geq 0 \; \text{of an LPP is:}\)

• A. Region A
• B. Region B
• C. Region C
• D. Region D

Answer 1

The Correct Option is C

To determine the feasible region represented by the constraints, we follow these steps:

Plotting the Constraints:

The constraints are:

\[4x + y \geq 80\]

\[x + 5y \geq 115\]

\[3x + 2y \leq 150\]

\[x, y \geq 0 \text{ (indicating the feasible region is in the first quadrant)}\]

Each constraint represents a line in the \( xy \)-plane.

Identifying the Feasible Region:

The region satisfying all the constraints is the shaded region bounded by the intersection of the lines.

Based on the plot provided, Region C is enclosed by these lines and represents the feasible solution set for the linear programming problem (LPP).

Verification:

Region C satisfies all the constraints, including the inequality \( 3x + 2y \leq 150 \), which bounds it from above.

Other regions do not satisfy all the constraints simultaneously.

Thus, the feasible region for the given LPP is represented by Region C.