The operations manager for a local bus company wants to decide whether he should purchase a small, medium, or large new bus for his company. He estimates that the annual profits (in $000) will vary depending upon whether passenger demand is low, moderate, or high, as follows.

-If he uses the maximum likelihood criterion,which size bus will he decide to purchase?
A)Small
B)Medium
C)Large
D)Either small or medium
E)Either medium or large

Question

The operations manager for a local bus company wants to decide whether he should purchase a small, medium, or large new bus for his company. He estimates that the annual profits (in $000) will vary depending upon whether passenger demand is low, moderate, or high, as follows.
 
-If he uses the maximum likelihood criterion,which size bus will he decide to purchase?
A)Small 
B)Medium 
C)Large 
D)Either small or medium 
E)Either medium or large

Quizplus · Accepted Answer

To use the maximum likelihood criterion, we need to choose the bus size that will generate the highest expected profit for each demand level. To calculate this, we multiply the demand level by the profit for each bus size and then choose the size with the highest total expected profit for all demand levels.

For the small bus:
- Low demand: 0 × 8 = 0
- Moderate demand: 3 × 10 = 30
- High demand: 6 × 12 = 72
Total expected profit: 0 + 30 + 72 = 102

For the medium bus:
- Low demand: 0 × 12 = 0
- Moderate demand: 4 × 16 = 64
- High demand: 5 × 16 = 80
Total expected profit: 0 + 64 + 80 = 144

For the large bus:
- Low demand: 2 × 15 = 30
- Moderate demand: 4 × 18 = 72
- High demand: 5 × 20 = 100
Total expected profit: 30 + 72 + 100 = 202

Therefore, the maximum likelihood criterion suggests that the operations manager should purchase the large bus, as it generates the highest expected profit for all demand levels.

The Operations Manager for a Local Bus Company Wants to Decide