Answer:
C = 6 is the minimum value
Step-by-step explanation:
We require a sketch of the constraints to determine the feasible region.
Sketch the following
2x + 3y = 6
with x- intercept = (3, 0) and y- intercept = (0, 2)
3x - 2y = 9
with x- intercept = (3, 0) and y- intercept = (0, - 4.5)
x + 5y = 20
with x- intercept = (20, 0) and y- intercept = (0, 4)
Solve 3x - 2y = 9 and x + 5y = 20 to find the point of intersection (5, 3)
The vertices of the feasible region are
(0, 2), (0, 4), (5, 3), (3, 0)
Evaluate the objective function C = 4x + 3y at each of the vertices
(0, 2) → C = 4(0) + 3(2) = 0 + 6 = 6 ← minimum value
(0, 4) → C = 4(0) + 3(4) = 0 + 12 = 12
(5, 3) → C = 4(5) + 3(3) = 20 + 9 = 29
(3, 0) → C = 4(3) + 3(0) = 12 + 0 = 12
Minimum value is C = 6 when x = 0 and y = 2
