Question

The maximum value of \( Z = 4x + y \) for a L.P.P. whose feasible region is given below is: 
 

• A. \( 50 \)
• B. \( 110 \)
• C. \( 120 \)
• D. \( 170 \)

Hint:

For L.P.P., always evaluate the objective function at all vertices of the feasible region.

Answer 1

The Correct Option is C

Step 1: Identify the corner points of the feasible region
From the graph, the vertices of the feasible region are: \[ A(0, 50), \, B(20, 30), \, C(30, 0). \]
Step 2: Substitute corner points into \( Z = 4x + y \)
Evaluate \( Z \) at each vertex: \[ Z_A = 4(0) + 50 = 50,\] \[\quad Z_B = 4(20) + 30 = 110,\] \[\quad Z_C = 4(30) + 0 = 120. \]
Step 3: Find the maximum value
The maximum value of \( Z \) occurs at \( C(30, 0) \), where \( Z = 120 \).
Step 4: Verify the options
The maximum value is \( 120 \), which corresponds to option (C).