JEE Main & Advanced
Mathematics
Linear Programming
Question Bank
Linear Programming
question_answer
The maximum value of \[z=3x+4y\] subject to the constraints \[x+y\le 40,\ x+2y\le 60,\ x\ge 0\] and \[y\ge 0\] is [MP PET 2002, 04]
A) 120
B) 140
C) 100
D) 160
Correct Answer:
B
Solution :
Given, \[P=3x+4y\] This graph has been draw from given constraints and maximum value of P will be at A or B or C . \[{{P}_{A}}={{P}_{(0,30)}}=3\times 0+4\times 30=120\] \[{{P}_{B}}={{P}_{(20,20)}}=3\times 20+4\times 20=140\] \[{{P}_{C}}={{P}_{(40,0)}}=3\times 40+0=120\] Therefore \[{{P}_{\max }}=140\].