Question

Minimize z = -3x + 4y 

x + 2y ≤ 8, 3x + 2y ≤ 12, x ≥ 0, y ≥ 0

Answer 1

We draw the lines x + 2y = 8 and 3x + 2y = 12 to determine the feasible region. The shaded region OCEBO is the feasible region. Vertices of the feasible region are O(0,0), C(4,0), E(2,3) and B(0,4).

Now, we calculate z = -3x + 4y at each vertices

At, (0,0), z = 0

At, (4,0), z = -12

At, (2,3), z = 6

At, (0,4), z = 16

Hence, minimum value of z is -12 at (4,0)