Linear Programming

Just look at two examples. Nothing special.

Answer : D

1) Make y as subject
2) Draw all the lines needed
3) Since y ≥ -x + 2, arrow point upwards
4) Since y ≤ -x + 6, arrow point downwards
5) Similar for the remaining
6) Then, the area being bounded is the solution.

Remarks: 

1) Dotted line is used when >/< is used instead of  ≥/≤  and dotted line is not included in the bounded region.
2) y ≥, point upwards
3) y ≤, point downwards

Answer : B

Just find all the coordinates of vertices of the polygon.
We have (0,0), (0,4), (2,3), (3,2), (4,0).
Then, we substitute each of them into the 3x + 2y and see which one is the greatest.