Linear Programming Question 75
Question: For the following feasible region, the linear constraints are
Options:
A) $ x\ge 0,\ y\ge 0,\ 3x+2y\ge 12,\ x+3y\ge 11 $
B) $ x\ge 0,\ y\ge 0,\ 3x+2y\le 12,\ x+3y\ge 11 $
C) $ x\ge 0,\ y\ge 0,\ 3x+2y\le 12,\ x+3y\le 11 $
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
The feasible region of a set of linear inequalities is the region in which all the inequalities are satisfied simultaneously.For option A, the constraints are:x≥0y≥03x+2y≥12x+3y≥11
These constraints mean that the feasible region is the area that lies in the first quadrant (since x≥0 and y≥0) and above the lines 3x+2y=12 and x+3y=11.For options B and C, the inequalities are not all ‘greater than or equal to’, which means the feasible region would not be the same as in option A.
Therefore, the correct answer is indeed Option A.
The solution isn’t necessarily “obvious” without understanding the concept of feasible regions in linear programming, but once you understand that, it becomes clear why Option A is the correct choice.
BETA
