The objective function is z=4x+7y.
The corner points of the bounded feasible region are (0,0), (3,0), and (0,3).
In linear programming, the maximum value of the objective function occurs at one of the corner points of the feasible region.
At point (0,0):
z=4(0)+7(0)
z=0
At point (3,0):
z=4(3)+7(0)
z=12
At point (0,3):
z=4(0)+7(3)
z=21
Comparing the values:
- At (0,0): z=0
- At (3,0): z=12
- At (0,3): z=21
Therefore, the maximum value of z is 21.