Feasible region (shaded) for a LPP is shown in Fig. 12.8.

Maximise Z = 5x + 7y.

Given:

Z=5x+7y

The shaded region OABD in the given figure is the feasible region is bounded, so, maximum value will occur at a corner point of the feasible region.

Corner Points are O (0, 0), A (7,0), B (3,4) and D (0,2)

Now we will substitute these values in Z at each of these corner points, we get

Hence, the maximum value of Z is 43 at the point (3,4).