JEE Main & Advanced
Mathematics
Linear Programming
Question Bank
Linear Programming
question_answer
To maximize the objective function \[z=2x+3y\] under the constraints \[x+y\le 30,\ x-y\ge 0,\ y\le 12,\] \[x\le 20,\] \[y\ge 3\] and \[x,\ y\ge 0\]
A) \[x=12,\ y=18\]
B) \[x=18,\ y=12\]
C) \[x=12,\ y=12\]
D) \[x=20,\ y=10\]
Correct Answer:
B
Solution :
The objective function is Max\[z=2x+3y\]. The vertices are \[A(20,\,10)\], \[B(18,\,12),C(12,\,12),D\]\[(3,\,3)\] and E (20, 3). Hence the maximum value of the objective function will be at (18, 12).