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, medium, or high, as follows: $$\begin{array} { | l | l | l | l | }
\hline \text { Bus } & { \text { DEMAND } } \
\hline & \text { LOW } & \text { MEDIUM } & \text { HIGH } \
\hline \text { Small } & 50 & 60 & 70 \
\hline \text { Medium } & 40 & 80 & 90 \
\hline \text { Large } & 20 & 50 & 120 \
\hline
\end{array}$$ If he uses the Laplace 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, medium, or high, as follows: $$\begin{array} { | l | l | l | l | } 
\hline \text { Bus } &   { \text { DEMAND } } \
\hline & \text { LOW } & \text { MEDIUM } & \text { HIGH } \
 \hline \text { Small } & 50 & 60 & 70 \
\hline \text { Medium } & 40 & 80 & 90 \
\hline \text { Large } & 20 & 50 & 120 \
\hline
\end{array}$$ If he uses the Laplace 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

The Laplace criterion assumes that all possible outcomes have an equal probability of occurring. Thus, we can calculate the expected profits for each size bus by taking the average of the profits for low, medium, and high demand scenarios.

For the small bus, the expected profit is:

(50 + 60 + 70) / 3 = 60

For the medium bus, the expected profit is:

(40 + 80 + 90) / 3 = 70

For the large bus, the expected profit is:

(20 + 50 + 120) / 3 = 63.33

Therefore, according to the Laplace criterion, the operations manager should choose the medium bus as it has the highest expected profit among the options.

The Operations Manager for a Local Bus Company Wants to Decide