Q. The maximum value of $\mu = 3x + 4y$, subjected to the conditions $x + y \leq 40,\ x + 2y \leq 60;x,\ y \geq 0$, is
A) 130
B) 140
C) 40
D) 120
Explanation
(b)
Feasible region is $OACBO$ and $\mu = 3x + 4y$
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At point $O(0,\ 0)$
$\mu = 0 + 0 = 0$
At point $A(40,\ 0)$
$\mu = 3(40) + 4(0) = 120$
At point $B(0,\ 30)$
$\mu = 0 + 4(30) = 120$
At point $C(20,\ 20)$
$\mu = 3(20) + 4(20) = 140$
$\therefore$ The maximum value at the point $C(20,\ 20)$ is 140
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.