--%>
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 : Compare the test results The grade

    The grade point averages of 61 students who completed a college course in financial accounting have a standard deviation of .790. The grade point averages of 17 students who dropped out of the same course have a standard deviation of .940. Do the data indicate a

    		•
  • Q : Explain Queuing theory Queuing theory :

    Queuing theory: • Queuing theory deals with the analysis of lines where customers wait to receive a service:

    Q : Correlation analysis and the regression

    1).  When you take out a mortgage, there are many different kinds of costs.  Usually the two largest are the interest rate (annual percentage that determines the size of your monthly payment) and the loan fee (a one-time percentage charged to you at the time

    		•
  • 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 : 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 : Hypothesis homework A sample of 9 days

    A sample of 9 days over the past six months showed that a clinic treated the following numbers of patients: 24, 26, 21, 17, 16, 23, 27, 18, and 25. If the number of patients seen per day is normally distributed, would an analysis of these sample data provide evidence that the variance in the numbe

    		•
  • Q : Assumptions in Queuing system

    Assumptions in Queuing system: • Flow balance implies that the number of arrivals in an observation period is equal to the

    		•
  • Q : Problem on queuing diagram Draw a 

    Draw a queuing diagram for the systems below and describe them using Kendall’s notation: A) Single CPU system <

    		•
  • Q : Sample Questions in Graphical Solution

    Solved problems in Graphical Solution Procedure, sample assignments and homework Questions: Minimize Z = 10x1 + 4x2 Subject to