--%>
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 : Help An experiment is conducted in

    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 : 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 : Data Description 1. If the mean number

    1. If the mean number of hours of television watched by teenagers per week is 12 with a standard deviation of 2 hours, what proportion of teenagers watch 16 to 18 hours of TV a week? (Assume a normal distribution.) A. 2.1% B. 4.5% C. 0.3% D. 4.2% 2. The probability of an offender having a s

    		•
  • 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 : OIL I need to product when oil will

    I need to product when oil will finish time (by years) for 6 countries if the keep their production (per day) in the same level. So, the 6 countries have fixed reserves and production 1. statistics for Bahrain Crude oil reserves (million barrels) = 124.6 be careful in million Crude oil producti

    		•
  • Q : Spss in Business and Management Please

    Please tell me the cost of this current assignment. Note : I do not want the Solutions but please tell me the price as the assignment is .. Is the cost 3 euro? Do you sell those questions?

    		•
  • 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 : Regression Analysis 1. A planning

    1. A planning official in the Texas Department of Community Affairs, which works in the office next to you, has a problem. He has been handed a data set from his boss that includes the costs involved in developing local land use plans for communities wi

    		•
  • Q : Probability how can i calculate

    how can i calculate cumulative probabilities of survival

    		•
  • Q : Networks of queues Networks of queues •

    Networks of queues • Typically, the flow of customers/request through a system may involve a number of different processing nodes.– IP packets through a computer network– Orders through a manufactur

    		•