As shown in the figure, OAED is the feasible region.
At A, y = 0 in equation 2x + y = 104 we get,
x = 52
This is a corner point A = (52, 0)
At D, x = 0 in equation x + 2y = 76 we get,
y = 38
This is another corner point D = (0, 38)
Now, solving the given equations x + 2y = 76 and 2x + y = 104 we have
2x + 4y = 152
2x + y = 104
(-)___(-)____(-)____
3y = 48 ⇒ y = 16
Using the value of y in the equation, we get
x + 2(16) = 76 ⇒ x = 76 – 32 = 44
So, the corner point E = (44, 16)
On evaluating the maximum value of Z, we get
From the above table it’s seen that the maximum value of Z is 196.
Therefore, the maximum value of the function Z is 196 at (44, 16).