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

Z = x + 9y

Constraints:

X $\ge$ 0
Y $\ge$0
X + 4y $\le$ 20
X + y $\le$ 18
2x + 2y $\le$ 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

Find the maximum value of the objective function and where it occurs, subject to the constraints:  
Objective function:
 
Z = x + 9y
 
Constraints:
 
X $\ge$ 0
Y $\ge$0
X + 4y $\le$ 20
X + y $\le$ 18
 2x + 2y  $\le$ 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 $\left( \frac { 21 } { 2 } , 0 \right)$ : $\frac { 21 } { 2 }$

Quizplus · Accepted Answer

The maximum value of the objective function Z = x + 9y, given the constraints, occurs at the point (0, 5) where Z = 45. This is determined by plotting the constraints on a graph, identifying the feasible region, and then applying the objective function to find the point in the feasible region where Z is maximized. The point (0, 5) satisfies all the given constraints and results in the highest value of Z.

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