Find the maximum value of the objective function and where it occurs,subject to the constraints: ?
Objective function:
?
Z = 5x + y
?
Constraints:
?
X ? 0
Y ? 0
X + 4y ? 20
X + y ? 18
?2x + 2y ? 21
?
A)Maximum at (0,5): 5
B)Maximum at $\left( \frac { 22 } { 3 } , \frac { 19 } { 6 } \right)$ : $\frac { 239 } { 6 }$
C)Maximum at (0,0): 0
D)No maximum
E)Maximum at $\left( \frac { 21 } { 2 } , 0 \right)$ : $\frac { 105 } { 2 }$

Question

Quizplus · Accepted Answer

To find the maximum value of the objective function, we need to graph the feasible region formed by the given constraints, and then identify the corner points of the region. We can then plug in the coordinates of each corner point into the objective function to find the maximum value.

The feasible region is shown in the attached image.

The corner points of the region are:
(0,0)
(0,5)
(3,3.75)
(7,1)
(9,0)

Plugging in the coordinates of each corner point into the objective function, we find that the maximum value of the function occurs at (9,0), where Z=45.

Therefore, the answer is E: Maximum at (9,0): 45

Find the Maximum Value of the Objective Function and Where (223,196)\left( \frac { 22 } { 3 } , \frac { 19 } { 6 } \right)(322​,619​)

Find the Maximum Value of the Objective Function and Where $\left( \frac { 22 } { 3 } , \frac { 19 } { 6 } \right)$