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?

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

According to the maximum likelihood criterion, the manager should choose the bus size that maximizes the probability of earning the highest profit for each passenger demand level.

For low demand, the large bus is the most profitable, with a probability of 0.4 of earning $20,000 and a probability of 0.6 of earning $0:

0.4 x $20,000 + 0.6 x $0 = $8,000

For moderate demand, the large bus is again the most profitable, with a probability of 0.6 of earning $30,000 and a probability of 0.4 of earning $10,000:

0.6 x $30,000 + 0.4 x $10,000 = $22,000

For high demand, the medium bus is the most profitable, with a probability of 0.7 of earning $45,000 and a probability of 0.3 of earning $25,000:

0.7 x $45,000 + 0.3 x $25,000 = $37,000

Therefore, the expected profit for each bus size is:

Small: 0.2 x $5,000 + 0.8 x $0 = $1,000
Medium: 0.3 x $15,000 + 0.7 x $37,000 = $30,800
Large: 0.4 x $8,000 + 0.6 x $22,000 + 0.8 x $0 = $17,600

Based on these calculations, the manager should choose the large bus, as it has the highest expected profit of $17,600.

The Operations Manager for a Local Bus Company Wants to Decide