Linear Programming Question 130
Question: The maximum value of $ z=3x+2y, $ subjected to the conditions $ x+2y\ge 2,x+2y\le 8,x,y\ge 0 $ is
Options:
32
24
40
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
Given: $ x+2y $
$ \geq 2 $ (1)
$ x+2y $
$ \leq 8 $ (2)
And $ x, y $
$ \ge 0 $
For equation (1) $ \frac{x}{2}+\frac{y}{1}=1 $ and for equation
(2) $ \frac{x}{8}+\frac{y}{4}=1 $
Given: $ z=3x+2y $
At point $ (2,0);z=3\times 2+0=6 $
At point $ (0,1);z=3\times 0+2\times 1=2 $
At point $ (8,0);z=3\times 8+2\times 0=24 $
At point $ (0,4);z=3\times 0+2\times 4=8 $
$ \therefore $ Maximum value of z is 24 at point (8, 0).
BETA
