Question
Mathematics Question on Linear Programming Problem
Minimise Z=x+2y
Subject to 2x+y≥3,x+2y≥6,x,y≥0.
Answer
The feasible region determined by the constraints,2x+y≥3,x+2y≥6,x≥0 and y≥0,is as follows.
The corner point of the feasible region are A(6,0),B(0,3).
The value of Z at these corner points are as follows.
Corner point Z=x+2y A(6,0)6 B(0,3)6
It can be seen that the value of Z at points A and B is same. If we take any other point such as (2,2)on line x+2y=6, then Z=6
Thus,the minimum value of Z occurs for more than 2 points.
Therefore, the value of Z is minimum at every point on the line,x+2y=6.