Q.
The feasible region for an LPP is shown in the given figure. Then, the minimum value of $Z=11 x+7 y$ is
Linear Programming
Solution:
The given feasible region is
Let $A, B$ and $C$ be the corner points of the feasible region which is bounded.
$\therefore$ The coordinates of $A$ are $(3,2)$.
The coordinates of $B$ are $(0,3)$.
and the coordinates of $C$ are $(0,5)$.
The given objective function is
$Z=11 x+7 y$
The values of $Z$ at the corner points are given by
Corner point
Corresponding value of $Z$
$(3,2)$
47
$(0,3)$
21
$(0,5)$
35
From the above table, we see that the minimum value of $Z$ is 21.
| Corner point | Corresponding value of $Z$ |
|---|---|
| $(3,2)$ | 47 |
| $(0,3)$ | 21 |
| $(0,5)$ | 35 |