What point in the feasible region minimizes the objective function?
The vertices in the feasible region are (0, 0), (0, 1), (1.5, 1.5), and (3, 0)
And the objective function C = 5x + 4y
To determine the point in the feasible region that minimizes the objective function, we need to calculate the value of the objective function at each vertex and find the minimum value.
Plug in the coordinates of each vertex into the objective function C = 5x + 4y:
1. At (0, 0):
C = 5(0) + 4(0) = 0
2. At (0, 1):
C = 5(0) + 4(1) = 4
3. At (1.5, 1.5):
C = 5(1.5) + 4(1.5) = 15 + 6 = 21
4. At (3, 0):
C = 5(3) + 4(0) = 15 + 0 = 15
The lowest value of the objective function is 0 at the point (0, 0). Therefore, the point (0, 0) in the feasible region minimizes the objective function.