## Related questions with answers

Myrtle Air Express decided to offer direct service from Cleveland to Myrtle Beach. Management must decide between a full price service using the company’s new fleet of jet aircraft and a discount service using smaller capacity commuter planes. It is clear that the best choice depends on the market reaction to the service Myrtle Air offers. Management developed estimates of the contribution to profit for each type of service based upon two possible levels of demand for service to Myrtle Beach: strong and weak. The following table shows the estimated quarterly profits (in thousands of dollars).

$\begin{matrix} \text{ } & \text{Demand} & \text{for Service}\\ \hline \text{Service} & \text{Strong} & \text{Weak}\\ \text{Full price} & \text{\$960} & \text{-\$490}\\ \text{Discount} & \text{\$670} & \text{\$320}\\ \end{matrix}$

a. What is the decision to be made, what is the chance event, and what is the consequence for this problem? How many decision alternatives are there? How many outcomes are there for the chance event? b. Suppose that management of Myrtle Air Express believes that the probability of strong demand is .7 and the probability of weak demand is .3. Use the expected value approach to determine an optimal decision. c. Suppose that the probability of strong demand is .8 and the probability of weak demand is .2. What is the optimal decision using the expected value approach?

Solution

VerifiedGiven:

$\begin{align*} V_{11}&=960 \\ V_{12}&=-490 \\ V_{21}&=670 \\ V_{22}&=320 \end{align*}$

Let

$d_1$=Full price

$d_2$=Discount

$s_1$=Strong

$s_2$=Weak

(a) The decision to be made is which service to use. That is, we need to decide between full price service or discount service, which implies that there are 2 decision alternatives.

The chance even is the type of demand, while there are 2 outcomes for the chance event: Strong and Weak.

The consequence for this problem is the estimated quarterly profit.

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