A graph of the constraint region is shown in the picture below.
The minimum value of the objective function is: C = [16].
In this exercise, we would graph the feasible region that is defined by the constraints and then, we would evaluate the objective function (C) at these vertices of the feasible region in order to find the minimum value.
Based on the points where the shaded regions overlap in the graph, we have the following vertices of the feasible region:
(0, 8), (7, 1), and (17/2, 0).
Now, we can evaluate the objective function C = 4x + 2y at these vertices as follows:
For the point (0, 8), we have;
C = 4(0) + 2(8)
C = 16
For the point (7, 1), we have;
C = 4(7) + 2(1)
C = 30
For the point (17/2, 0), we have;
C = 4(17/2) + 2(0)
C = 34
In conclusion, minimum value of this objective function C = 4x + 2y based on the given constraints is 16.
Complete Question;
Find the minimum value of C = 4x + 2y subject to the following constraints:
x + y ≥ 8
2x + 3y ≥ 17
x ≥ 0
y ≥ 0
C = [?]