First, we'd need to find the feasible region which is bounded by the constraints 2 ≤ x ≤ 6, 1 ≤ y ≤ 5 and x + y ≤ 8. Let's graph all of them and we'll get the feasible region as unshaded in the attached image. To find the maximum for p = 3x + 2y, we'll plug the coordinates of the vertices in and compare them.
p(6,1) = 3(6) + 2(1) = 20
p(2,1) = 3(2) + 2(1) = 8
p(2,5) = 3(2) + 2(5) = 16
p(3,5) = 3(3) + 2(5) = 19
p(6,2) = 3(6) + 2(2) = 22
So the maximum value of p is 22 as x = 6 and y = 2.
