Maximize the object function subject to the constraints
A) The maximum value is 24 along the line segment connection
B) The maximum value is 30 along the line segment connection
C) The maximum value is 30 along the line segment connection
D) The maximum value is 24 along the line segment connection
E) The maximum value is 30 along the line segment connection

Question

Maximize the object function  subject to the constraints 
A) The maximum value is 24 along the line segment connection 
B) The maximum value is 30 along the line segment connection 
C) The maximum value is 30 along the line segment connection 
D) The maximum value is 24 along the line segment connection 
E) The maximum value is 30 along the line segment connection

Quizplus · Accepted Answer

We need to locate the corner points of the feasible region and check the objective function value at each corner point to determine the maximum value. 
The corner points are (0,0), (0,5), (2,6), and (6,0). 
When we substitute each of these points into the objective function, we get the following values: 
- (0,0): 0 
- (0,5): 25 
- (2,6): 30 
- (6,0): 36

Therefore, the maximum value is 30 and it occurs at point (2,6), which is on the line segment connection between (0,5) and (6,0). Choice C correctly identifies this as the maximum value and the line segment as the location where it occurs.

Maximize the Object Function Subject to the Constraints