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.
The vertices of the feasible region are determined from the graph to be: \[A(0, 50), \, B(20, 30), \, C(30, 0).\]
Step 2: Substitute corner points into the objective function \( Z = 4x + y \).
The objective function is evaluated 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: Determine the maximum value.
The maximum value of \( Z \) is \( 120 \), which occurs at vertex \( C(30, 0) \).
Step 4: Match with options.
The maximum value of \( 120 \) corresponds to option (C).