Find the minimum and maximum values of the objective function and where they occur, subject to the constraints
A) The minimum value is 0 at and the maximum value is 32 at
B) The minimum value is 0 at and the maximum value is 32 at
C) The minimum value is 0 at and the maximum value is 32 at
D) The minimum value is 0 at and the maximum value is 32 at
E) The minimum value is 0 at and the maximum value is 32 at

Question

Find the minimum and maximum values of the objective function  and where they occur, subject to the constraints  
A) The minimum value is 0 at and the maximum value is 32 at 
B) The minimum value is 0 at and the maximum value is 32 at 
C) The minimum value is 0 at and the maximum value is 32 at 
D) The minimum value is 0 at and the maximum value is 32 at 
E) The minimum value is 0 at and the maximum value is 32 at

Quizplus · Accepted Answer

To find the minimum and maximum values of the objective function, we can use the corner point method. We first graph the system of inequalities and find the corner points where the lines intersect:
- Intersection of 3x + y = 0 and x = 0: (0,0)
- Intersection of 3x + y = 24 and x = 8: (8,0)
- Intersection of x + y = 8 and x = 0: (0,8)

Next, we evaluate the objective function at each corner point:
- At (0,0): 11(0) + 8(0) = 0
- At (8,0): 11(8) + 8(0) = 88
- At (0,8): 11(0) + 8(8) = 64

Therefore, the minimum value is 0 at (0,0) and the maximum value is 88 at (8,0). The answer choices that include these values are A and D. However, D has incorrect coordinates for the corner points, so the answer is A.

Find the Minimum and Maximum Values of the Objective Function