In the given figure, it’s seen that the feasible region is ABCA. The corner points are C(0, 3), B(0, 5) and for A, we have to solve equations
x + 3y = 9 and
x + y = 5
(-)_(-)_(-)
2y = 4 ⇒ y = 2
And, putting value of y in the equation we get x = 3
So, the corner point is A(3, 2).
Now, evaluating the value of Z we get
From the above table it’s seen that the minimum value of Z is 21.
Therefore, the minimum value of the function Z is 21 at (0, 3).