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 feels the chances of low, medium, and high demand are 30 percent, 30 percent, and 40 percent respectively, what is the expected annual profit for the bus that he will decide to purchase?
A) $15,000
B) $61,000
C) $69,000
D) $72,000
E) $87,000

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 feels the chances of low, medium, and high demand are 30 percent, 30 percent, and 40 percent respectively, what is the expected annual profit for the bus that he will decide to purchase?
A) $15,000
B) $61,000
C) $69,000
D) $72,000
E) $87,000

Quizplus · Accepted Answer

To find the expected annual profit for each bus, we need to multiply the profit for each level of demand by the probability of that level of demand occurring, and then sum the results:

Expected profit for Small bus: 
(50 x 0.3) + (60 x 0.3) + (70 x 0.4) = $58,000

Expected profit for Medium bus: 
(40 x 0.3) + (80 x 0.3) + (90 x 0.4) = $70,000

Expected profit for Large bus: 
(20 x 0.3) + (50 x 0.3) + (120 x 0.4) = $72,000

Therefore, the best choice for the bus company would be to purchase the Large bus, which has the highest expected profit of $72,000.

The Operations Manager for a Local Bus Company Wants to Decide