Problem 13-09 (Algorithmic) Myrtle Air Express decided to offer direct service f
ID: 364511 • Letter: P
Question
Problem 13-09 (Algorithmic)
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):
What is the decision to be made, what is the chance event, and what is the consequence for this problem?
The input in the box below will not be graded, but may be reviewed and considered by your instructor.
How many decision alternatives are there?
Number of decision alternatives =
How many outcomes are there for the chance event?
Number of outcomes =
Explanation / Answer
Hi,
Thanks for the question.
In this question, Myrtle has launched a new service and they have to decide which kind of service they want to give while maximizing their profits.
Answer 1)
They Myrtle has two options of prices to give to its customers. Whether they can offer full price or the discounted price services. So Myrtle only has to make this decision as to what kind of service they should provide to the customers.
Chance event can be described as any event that happens without any prior cause. In this case, the demand is a chance event. Whether the demand will be strong or weak, is the chance event.
Consequences means the results. The impact or consequences of chance event will be the profits that Myrtle will make. Since, in case of either kind of demand, the profit margins are different.
Answer 2)
As explained in the above answer, company has to make a decision between full price or discounted price services. That means there are only two decision alternatives.
As explained, Chance event in this scenario is the demand. According to the data given, there are only two kind of demands - strong and weak demand. So there are only two outcomes for the chance event.
Answer 3)
To calculate this, we must need the slope and intercept to put the two equations on the graph.
Lets suppose we have probability of x for the strong demand. Since the probability of any chance event ranges between 0 to 1, the probability for weak demand is (1-x)
Profit (full price) = (probability of strong probability * profit) + (probability of weak probability * profit)
= (x* 1260) + (1-x)*(-440)
= 1260x - 440 + 440x
= 1700x - 440
Profit (Discounted) = (probability of strong probability * profit) + (probability of weak probability * profit)
= (x* 990) + (1-x)*420
= 990x + 420 - 420x
= 570x + 420
To calculate the value of p, Profit(Full price) = Profit(discounted)
1700x - 440 = 570x + 420
1700x - 570x = 420 + 440
1130x = 870
x= (870/1130)
x = 0.7699
With this value of probability we can conclude that at the probability of 0.7699, the profits of both the situations is equal.
If the value of probability of strong demand is less than 0.7699, then profits for discounted price will be more and would be best choice.
for discounted price, the range is = 0 to 0.7699
for full price, the range is = 0.7699 to 1