Question

For the feasible region shown below, the non-trivial constraints of the linear programming problem are 

• A. $x+y\le6,\; x+3y\le9$
• B. $x+y\le6,\; x+3y\ge9$
• C. $x+y\ge6,\; x+3y\le9$
• D. $x+y\ge6,\; 3x+y\le9$

Hint:

In graph-based Linear Programming questions, first determine the line equations from intercepts and then check which side of the line contains the shaded feasible region.

Answer 1

The Correct Option is A

Step 1: Understand the graph.
From the given figure we observe two boundary lines forming the feasible region.
The shaded region lies below both lines.
Thus the inequalities will be of the form \(\le\).
Step 2: Identify the first line.
The first line passes through the intercepts:
\[ (0,6) \quad \text{and} \quad (6,0) \] Equation of this line is
\[ x+y=6 \] Since the region is below the line
\[ x+y\le6 \] Step 3: Identify the second line.
The second line passes through the intercepts:
\[ (0,3) \quad \text{and} \quad (9,0) \] Equation of this line becomes
\[ x+3y=9 \] Again the feasible region lies below this line
\[ x+3y\le9 \] Step 4: Combine the constraints.
Thus the two non-trivial constraints are
\[ x+y\le6 \] \[ x+3y\le9 \] Step 5: Conclusion.
Therefore the correct pair of inequalities representing the feasible region is
\[ x+y\le6,\quad x+3y\le9 \] Final Answer: $\boxed{x+y\le6,\; x+3y\le9}$