Answer:
C = 14
Explanation:
Sketching the inequalities
x = - 2 and x = - 4 are vertical lines
y = 1 and y = 6 are horizontal lines
The vertices at the points of intersection are
(- 4, 6), (- 2, 6), (- 4, 1), (- 2, 1)
Evaluate the objective function at each vertex
(- 4, 6) → C = 5(- 4) + 4(6) = - 20 + 24 = 4
(- 2, 6) → C = 5(- 2) + 4(6) = - 10 + 24 = 14 ← maximum value
(- 4, 1) → C = 5(- 4) + 4(1) = - 20 + 4 = - 16
(- 2, 1) → C = 5(- 2) + 4(1) = - 10 + 4 = - 6
Maximum value is C = 14 when x = - 2 and y = 6