Answer:
C = 14 is the minimum value
Step-by-step explanation:
Sketch the inequalities using
2x + y = 20
with x- intercept = (10, 0) and y- intercept = (0, 20)
2x + 3y = 36
with x- intercept = (18, 0) and y- intercept = (0, 12)
Solve 2x + y = 20 and 2x + 3y = 36 simultaneously to find
The point of intersection at (6, 8))
The vertices of the feasible region are at
(0, 20), (6, 8), (18, 0)
Evaluate the objective function C = x + y at each of the vertices
(0, 20) → C = 0 + 20 = 20
(6, 8) → C = 6 + 8 = 14 ← minimum value
(18, 0) → C = 18 + 0 = 18
Minimum value is C = 14 when x = 6 and y = 8
