Find the maximum value of the objective function and where it occurs, subject to the indicated constraints.
Objective function:

Z = 4x + 5y

Constraints:

X ≥ 0
3x - y ≤ 9
2x + 3y ≥ 6
X + 4y ≤ 16

A)Maximum at (3, 0): 12
B)Maximum at (3, 4): 32
C)Maximum at (4, 3): 31
D)Maximum at (0, 4): 20
E)Maximum at (0, 2): 10

Question

Find the maximum value of the objective function and where it occurs, subject to the indicated constraints. ​
Objective function:
​
Z = 4x + 5y
​
Constraints:
​
X ≥ 0
​3x - y ≤ 9
2x + 3y ≥ 6
X + 4y ≤ 16
​​  ​
A)Maximum at (3, 0): 12 
B)Maximum at (3, 4): 32 
C)Maximum at (4, 3): 31 
D)Maximum at (0, 4): 20 
E)Maximum at (0, 2): 10

Quizplus · Accepted Answer

By graphing the constraints and finding the feasible region, we can see that the vertices of the feasible region are (0,2), (3,0), and (4,3). We then plug in these coordinates into the objective function to find the maximum value.

Z(0,2) = 5(2) = 10
Z(3,0) = 4(3) = 12
Z(4,3) = 4(4) + 5(3) = 31

Therefore, the maximum value is 31 and it occurs at (4,3).

Find the Maximum Value of the Objective Function and Where