Linear Programming Question 66
Question: 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]
Options:
A) 120
B) 140
C) 100
D) 160
Show Answer
Answer:
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 $ .
BETA
