Question

The feasible region for an LPP is shown below. If $Z=4x+y$, then the minimum value of $Z$ is

• A. 4
• B. 3
• C. 2
• D. Does not exist

Answer 1

Answer: (B)

The given feasible region is

From the above graph, we see that $ABC$ is the feasible region which is unbounded and its corner points are $A(0,3),B(2,1),C(4,0)$.
The given objective function is $Z=4x+y$
The values of $Z$ at the corner points are given by

Corner point	Corresponding value of $Z$
$(0,3)$	3
$(2,1)$	9
$(4,0)$	16

From the above table, we see that the minimum value of $Z$ is
3 . Now, to check, if $Z=3$ is the minimum value, we draw the line $4x+y=3$
Since, the open half plane $4x+y<3$ does not intersect the feasible region at any point. Hence, minimum value of $Z$ is 3.