Question

The fesible region for a LPP is shown in following figure. Find the minimum value of Z =11x +7y.

Answer 1

From the figure, it is clear that feasible region is bounded with coordinates of corner points as (0,3),(3,2) and (0,5). Here, Z =11x+7y.

$\because x+3y=9$ and x + y =5
$\Rightarrow 2y=4$
$\therefore y=2$ and x =3
So, intersection points of x + y =5 and x +3y =9 is (3,2).
$\begin{array}{cc}\text{Corner points}& \text{Corresponding value of Z}\\ (0,3)& 21\leftarrow \text{Manimum}\\ (3,2)& 47\\ (0,5)& 35\end{array}$
Hence, the manimum value of Z is 21 at (0,3).