#### Answer

The objective function has maximum value 24
at (6,0)

#### Work Step by Step

The region that is defined by the constraints is
* to the right of x=0 (the y=axis),
* above the line y=0 (the x-axis),
* below the line 2x+3y=12
(for this line, when x=0, y=4 and when y=0, x=6)
* above the line x+y=3,
(for this line, when x=0, y=3 and when y=0, x=3)
The region is shaded red on the image below.
The corners are (0,4), (0,3), (3,0) and (6,0).
Calculating the objective function z=4x+y in each corner point,
(table in step 6 of the image)
we find that
the objective function has maximum value 24
at (6,0)