--%>
Assignment Help - homework help

Computing Average revenue using Standard deviation

Can anyone help me in the illustrated problem? The airport branch of a car rental company maintains a fleet of 50 SUVs. The inter-arrival time between the requests for an SUV is 2.4 hrs, on an average, with a standard deviation of 2.4 hrs. There is no indication of a systematic arrival pattern over the course of a day. Suppose that, if all SUVs are rented, then customers are willing to wait until there is an SUV available. The SUV is rented, on an average, for 3 days, with a standard deviation of one day.

a. Determine the average number of SUVs parked in the company’s lot?

b. By using a marketing survey, the company has discovered that if it decreases its daily rental price of $80 by $25, the average demand would rise to 12 rental requests per day and the average rental duration will become 4 days. Supposing that the standard deviation values stay unchanged, should this company adopt this latest pricing policy? Give an analysis!

c. Determine the average time a customer has to wait to rent an SUV? Please employ the initial parameters instead of the information in (b).

d. How would the waiting time change when the company decides to limit all the SUV rentals to exactly 4 days? Suppose that if such a restriction is imposed, the average inter-arrival time will rise to 3 hours, with the standard deviation changing to 3 hrs.

E

Expert

Verified

a) We know that a = 2.4 hours, p = 24 x 3 = 72 hours, CVa = (2.4/2.4) = 1, CVp = (24/72) = 0.33, and m = 50 cars

Percentage of cars used = (1/a)/(m/p) = (1/2.4)/(50/72) = 60%

Therefore, cars in use = 50 x 0.6 = 30

So, cars in parking lot = 20

b) a = 2, p = 96 hours,

Therefore, Percentage of cars used = (1/a)/ (m/p) = (1/2)/ (50/96) = 96%

So, average number of cars used = 50 x 0.96 = 48

Average revenue initially = 80 x 30 = $2400
Average revenue now = 48 x 55 = $2640

Therefore, the company should take the proposed step.

c) a = 2.4 hours, p = 24 x 3 = 72 hours, CVa = (2.4/2.4) = 1, CVp = (24/72) = 0.33, and m = 50 cars,

Waiting time = (p/m)(u^[{2(m+1)}1/2 – 1]/1-u)[CVa2 + CVp2/2]

= (72/50) (0.6^ {(102)1/2 – 1}/0.4) (1 + (0.33)2/2)

= 1.44 x (0.6) ^9 x 0.55/0.4 = 0.02 hours = 1.2 minutes

d) a = 3 hours, p = 24 x 4 =96 hours, CVa = (3/3) = 1, CVp = (24/96) = 0.25, and m = 50 cars

Percentage of cars used = (1/a)/(m/p) = (1/3)/(50/96) = 64%

Waiting time = (p/m) (u^ [{2(m+1)}1/2 – 1]/1-u) [CVa2 + CVp2/2]

= (96/50) (0.64^ {(102)1/2 – 1}/0.36) (1 + (0.25)2/2)

= 1.92 x (0.64) ^9 x 0.53/0.36 = 0.05 hours = 3 minutes

   Related Questions in Basic Statistics

  • Q : Problems on ANOVA We are going to

    We are going to simulate an experiment where we are trying to see whether any of the four automated systems (labeled A, B, C, and D) that we use to produce our root beer result in a different specific gravity than any of the other systems. For this example, we would l

    		•
  • Q : STATISTICS Question This week you will

    This week you will analyze if women drink more sodas than men.  For the purposes of this Question, assume that in the past there has been no difference.  However, you have seen lots of women drinking sodas the past few months.  You will perform a hypothesis test to determine if women now drink more

    		•
  • Q : Simplified demonstration of Littles Law

    Simplified demonstration of Little’s Law:

    Q : What is Forced Flow Law Forced Flow Law

    Forced Flow Law: • The forced flow law captures the relationship between the various components in the system. It states that the throughputs or flows, in all parts of a system must be proportional t

    		•
  • Q : Hw An experiment is conducted in which

    An experiment is conducted in which 60 participants each fill out a personality test, but not according to the way they see themselves. Instead, 20 are randomly assigned to fill it out according to the way they think a parent sees them (i.e. how a parent would fill it out to describe the participant

    		•
  • Q : State the hypotheses At Western

    At Western University the historical mean of scholarship examination score for freshman applications is 900. Population standard deviation is assumed to be known as 180. Each year, the assistant dean uses a sample of applications to determine whether the mean ex

    		•
  • Q : Safety and Liveness in Model Checking

    Safety and Liveness in Model Checking Approach; •? Safety: Nothing bad happens •? Liveness: Something good happens •? Model checking is especially good at verifying safety and liveness properties    –?Concurrency i

    		•
  • Q : Designing a system What are the

    What are the questions that comes into mind when designing a system?

    		•
  • Q : Computers playing games How Computers

    How Computers playing games can be categorized according to different dimensions?

    		•
  • Q : Principles of data analysis For the

    For the data analysis project, you will address some questions that interest you with the statistical methodology we are learning in class. You choose the questions; you decide how to collect data; you do the analyses. The questions can address almost any topic,

    		•