Find the maximum value of the objective function and where it occurs,subject to the constraints: ?
Objective function:
?
Z = x + 9y
?
Constraints:
?
X ? 0
Y ? 0
X + 4y ? 20
X + y ? 18
?2x + 2y ? 21
?
A)Maximum at (0,5): 45
B)Maximum at $\left( \frac { 22 } { 3 } , \frac { 19 } { 6 } \right)$ : $\frac { 215 } { 6 }$
C)No maximum
D)Maximum at (0,0): 0
E)Maximum at $\left( \frac { 21 } { 2 } , 0 \right)$ : $\frac { 21 } { 2 }$

Question

Quizplus · Accepted Answer

The feasible region is bounded and therefore, the maximum value of the objective function can be achieved. Using graphical method, we can find that the solution lies at the intersection of X+y = 18 and x+4y=20, which is (0,5) and the maximum value of the objective function at this point is 45. Therefore, the best choice is A.

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 $\left( \frac { 22 } { 3 } , \frac { 19 } { 6 } \right)$