Question

Determine the maximum value of Z = 3x + 4y if the feasible region (shaded) for a LPP is shown in Fig.

Answer 1

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).