Consider an objective function Z(x1, x2) = 3x1 + 9x2 and

Consider an objective function Z(x₁, x₂) = 3x₁ + 9x₂ and the constraints
x₁ + x₂ ≤ 8
x₁ + 2x₂ ≤ 4
x₁ ≥ 0, x₂ ≥ 0
The maximum value of the objective function is __________.

Z = 3x₁ + 4x₂
x₁ + x₂ ≤ 8
x₁ + 2x₁ ≤ 4
x₁, x₁ ≥ 0

At point A:
z = 3 (4) +9 (0) = 12
At point B:
z = 3 (0) + 9 (2) = 18