f5 Math question

(1) 2x - y - 3 > 0 ...........(1)
x + 2y + 1 > 0 .........(2)
x < 3 .....................(3)
From (1) and (2)
2x - y - 3 = 0
2x + 4y + 2 = 0
(2x + 4y + 2) - (2x -y - 3) = 0
5y + 5 = 0, y = - 1 and x = 1 . The intersecting point is ( 1, - 1).
P = 2(1) + 5(-1) = 2 - 5 = - 3
From (2) and (3)
x = 3, y = - 2. (3, - 2)
P = 2(3) + 5(-2) = 6 - 10 = - 4
From (1) and (3)
x = 3, y = 3. (3,3)
P = 2(3) + 5(3) = 21.
So P max. = 21, P min. = - 4.
(2)
Similar to the above, we can find the interesecting points be (0, 1), (0, 4) and (6, 3).
P = 2(0) + 4(1) = 4
P = 2(0) + 4(4) = 16
P = 2(6) + 4(3) = 24
so P max. = 24, P min. = 4.
(3)
The intersecting points are ( 4,3), ( 4, -3) and ( 0, 6)
P = - 4 + 3(3) = 5
P = - 4 + (-3) = - 7
P = - 0 + 3(6) = 18
so P max = 18, P min = - 7.