Linear Programming Question 77
Question: The solution set of the inequation $ 2x+y>5 $ , is
Options:
A) Half plane that contains the origin
B) Open half plane not containing the origin
C) Whole xy-plane except the points lying on the line $ 2x+y=5 $
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
The inequality
$2x+y>5$
represents a half-plane in the xy-plane.
To determine which half-plane it represents, we can rearrange the inequality to the form
$y>−2x+5$ .
This is the equation of a line with a negative slope (-2) and y-intercept (5).
The inequality sign “>” indicates that we are looking at the area above this line.
The origin (0,0) does not satisfy the inequality because substituting x=0 and y=0 into the inequality gives 0 > 5, which is not true.
Therefore, the solution set of the inequality is an open half-plane not containing the origin, which corresponds to Option B.
BETA
