Question

In: Statistics and Probability

Piotr Banasiewicz is a self-employed plumber who offers a 24-hour emergency service. For most of the...

Piotr Banasiewicz is a self-employed plumber who offers a 24-hour emergency service. For most of the year, calls arrive randomly at a rate of six a day. The time he takes to travel to a call and do the repair is randomly distributed with a mean of 90 minutes. Forecasts for February suggest cold weather and last time this happened Piotr received emergency calls at a rate of 18 a day. Because of repeat business, Piotr is anxious not to lose a customer and wants the average waiting time to be no longer in February than during a normal month. How many assistants should he employ to achieve this? • Assume a Single-Server model. • Ignore the stated Repair Time of 90 minutes. Instead, assume theRepair Time is 80 minutes. • Ignore the Arrival Rate of 6 per day. Instead, assume the Arrival Rateis 7 per day • In addition to the questions in the stated problem, determine the following: o Average server utilization o Average number of customers in the queue (Lq) o Average number of customers in the system (L) o Average waiting time in the queue (Wq) – express in days, hoursand minutes. o Average waiting time in the system (W) ) – express in days, hoursand minutes. o Probability there is 0 units in the system (P0) o Probability of "n" units in system with n=0 to up to n=20. o Probability of more than "n" units in system with n=0 to up to n=20. • Ignore the “How many assistants should he employ to achieve this?” question. • Instead, determine what the minimum Service Rate in customers per day should be for February, in order to maintain or improve the average waiting time (Wq) for the rest of the year. Please give step by step instructions on excel with formulas on how to solve.

Expert Solution

Average server utilization = 7*80 / 24*60 = 38.89%

Average number of customers in the queue (Lq) = 7 - 1 = 6

Average number of customers in the system (L) = 7

Average waiting time in the queue (Wq) – express in days, hoursand minutes = 80/person

Average waiting time in the system (W) ) – express in days, hoursand minutes = 80*6 = 480 minutes

Probability there is 0 units in the system (P0) = 1/7 (when last person is not in the queue)

For the above question we will apply M/M/1 queuing model.

As it is stated that it it single server model.So he can't employ any worker. He should be only server.

The following formula will be used

1. Average number of customers in the system

2. Average number of customers in the waiting line

3. Average waiting time in the system

4. Average waiting time in the queue

5. Utilization Factor

6. Probability of having n customers in the service system

Case 1)

Poisson call arrivals( = 6 per day) = = 0.0042 per minute .

Exponentially distributed Service time with rate( = 90 per minutes)= = 90

Case 2)

Poisson call arrivals( = 7 per day) = = 0.0049 per minute .

Exponentially distributed Service time with rate( = 90 per minutes)= = 80

Case 3) The minimum Service Rate in customers per day should be for February, in order to maintain or improve the average waiting time (Wq) for the rest of the year.

In february,Poisson call arrivals( = 18 per day) = = 0.0042 per minute , we have to estimate in order to maintain or improve . So,

The minimum Service rate should be 1.00212 in minutes.

orchestra answered 1 year ago

Phil is a self employed plumber and his wife, Lauren, is a full-time employee for the...

Phil is a self employed plumber and his wife, Lauren, is a full-time employee for the University. Lauren has health insurance from a qualified plan provided by the University, but Phil has chosen to purchase his own health insurance rather than participate in Lauren's plan. Besides paying $5,400 for his health insurance premiums, Phil also pays the following expenses associated with his plumbing business: Plumbing tools and supplies $1,300 Rent on Phil's plumbing shop 6,250 Transportation between Phil's shop and...

1. Scott is a self-employed plumber and his wife, Emily, is a full-time employee for a...

1. Scott is a self-employed plumber and his wife, Emily, is a full-time employee for a University. Emily has health insurance from a qualified plan provided by the University, but Scott has chosen to purchase his own health insurance rather than participate in Emily's plan. Besides paying $5,590 for his health insurance premiums, Scott also pays the following expenses associated with his plumbing business: Plumbing tools and supplies $1,490 Rent on Scott's plumbing shop 6,440 Transportation between Scott's shop and various...

Salim, a self-employed plumber, received the following income in 2017/2018: Building society interest £ 4,200 Dividends...

Salim, a self-employed plumber, received the following income in 2017/2018: Building society interest £ 4,200 Dividends from a UK company £ 3,800 Trading Income £ 80,000 He paid allowable interest of £3,000 on 15 August 2017/2018. The following tax rates are applicable during the fiscal year. BAND CATEGORY TAX RATE OTHER INCOME Basic rate 0 - £37,400 20% Higher rate 37401-150,000 40% SAVING INCOME Starting rate 0 - £2,440 10% Basic rate 2441-37400 20% Higher rate 37401-150,000 40% DIVIDEND...

1.11 You are the administrator of a large metropolitan hospital that operates the only 24-hour emergency...

1.11 You are the administrator of a large metropolitan hospital that operates the only 24-hour emergency room in the area. You must schedule attending physicians, resident physicians, nurses, laboratory, and support personnel to operate this facility effectively. a. What measures of effectiveness do you think patients use to evaluate the services that you provide? b.How are forecasts useful to you in planning services that will maximize these measures of effectiveness? c.What planning horizon do you need to use? Does this...

Smithers is a self-employed individual who earns $33,000 per year in self-employment income. Smithers pays $2,100...

Smithers is a self-employed individual who earns $33,000 per year in self-employment income. Smithers pays $2,100 in annual health insurance premiums (not through an exchange) for his own medical care. In each of the following situations, determine the amount of the deductible health insurance premium for Smithers before any AGI limitation. a. Smithers is single and the self-employment income is his only source of income. b. Smithers is single, but besides being self-employed, Smithers is also employed part-time by SF...

Anytown USA Bank prides itself on being very responsive to its customers. It offers a 24-hour...

Anytown USA Bank prides itself on being very responsive to its customers. It offers a 24-hour staffed customer care center with a toll-free number. Over the past year, there has been a significant decline in calls and a corresponding increase in email service requests. As Information Security Officer (ISO), you are very concerned that customerinformation classified as “protected” is being sent via email or email attachments. You have requested a meeting with the Director of IT to explore “secure email”...

Rita is a self-employed taxpayer who turns 39 years old at the end of the year...

Rita is a self-employed taxpayer who turns 39 years old at the end of the year (2018). In 2018, her net Schedule C income was $288,000. This was her only source of income. This year, Rita is considering setting up a retirement plan. What is the maximum amount Rita may contribute to the self-employed plan in each of the following situations? a. She sets up a SEP IRA. Maximum contribution b. She sets up an individual 401(k). Maximum contribution

Reggie is a self-employed taxpayer who turns 59 years old at the end of the year...

Reggie is a self-employed taxpayer who turns 59 years old at the end of the year (2018). In 2018, his net Schedule C income was $300,000. This was his only source of income. This year, Reggie is considering setting up a retirement plan. What is the maximum amount he may contribute to the self-employed plan in each of the following situations? a. He sets up a SEP IRA. b. He sets up an individual 401(k).

Elvira is a self-employed taxpayer who turns 42 years old at the end of the year...

Elvira is a self-employed taxpayer who turns 42 years old at the end of the year (2019). In 2019, her net Schedule C income was $130,000. This was her only source of income. This year, Elvira is considering setting up a retirement plan. What is the maximum amount Elvira may contribute to the self-employed plan in each of the following situations? (Round your intermediate calculations and final answers to the nearest whole dollar amount.) Problem 13-77 Part a a. She...

Hope is a self-employed taxpayer who turns 54 years old at the end of the year...

Hope is a self-employed taxpayer who turns 54 years old at the end of the year (2018). In 2018, her net Schedule C income was $130,000. This was her only source of income. This year, Hope is considering setting up a retirement plan. What is the maximum amount Hope may contribute to the self-employed plan in each of the following situations? a. She sets up a SEP IRA. b. She sets up an individual 401(k).