Question

Question 1 )

From historical data, Harry’s Car Wash estimates that dirty cars arrive at the rate of 8 cars per hour all day Saturday. With a crew working the wash line, harry figures that car can be cleaned at the rate of one every 6 minutes. One car at a time cleaned in this example of a single-channel waiting line. Assuming Poisson arrival and exponential service times, find the

1- Average number of cars in line.

2- Average time a car waits before it is washed.

3- Average time a car spends in the service system.

4- Utilization rate of the car wash.

5 - Probability that no car are in the system.

Question 2 )

Woofer Pet Food produces a low-calorie dog food for overweight dogs. This product is made from beef products and grain. Each pound of beef costs $0.80, and each pound of grain costs $0.50. A pound of the dog food must contain at least 10 units of Vitamin 1 and 12 units of Vitamin 2. A pound of beef contains 5 units of vitamin 1 and 7 units of vitamin 2. A pound of grain contains 6 units of vitamin 1 and 9 unites of vitamin 2. Formulate this as an LP problem to minimize the cost of the dog food. How many pounds of beef and grain should be included in each pound of dog food? What is the cost and vitamin content of final product?

From historical data, Harry’s Car Wash estimates that dirty cars arrive at the rate of 8 cars per hour all day Saturday. With a crew working the wash line, harry figures that car can be cleaned at the rate of one every 6 minutes. One car at a time cleaned in this example of a single-channel waiting line. Assuming Poisson arrival and exponential service times, find the

Average number of cars in line.

Average time a car waits before it is washed.

Average time a car spends in the service system.

Utilization rate of the car wash.

Probability that no car are in the system.

Woofer Pet Food produces a low-calorie dog food for overweight dogs. This product is made from beef products and grain. Each pound of beef costs $0.80, and each pound of grain costs $0.50. A pound of the dog food must contain at least 10 units of Vitamin 1 and 12 units of Vitamin 2. A pound of beef contains 5 units of vitamin 1 and 7 units of vitamin 2. A pound of grain contains 6 units of vitamin 1 and 9 unites of vitamin 2. Formulate this as an LP problem to minimize the cost of the dog food. How many pounds of beef and grain should be included in each pound of dog food? What is the cost and vitamin content of final product?

Answer #1

Exercise 11.2.5 Customers arrive at Bunkey’s car wash service at
a rate of one every 20 minutes and the average time it takes for a
car to proceed through their single wash station is 8 minutes.
Answer the following questions under the assumption of Poisson
arrivals and exponential service.
(a) What is the probability that an arriving customer will have
to wait?
(b) What is the average number of cars waiting to begin their
wash?
(c) What is the probability...

In a car pressure wash the average arrival rate is 12 cars per
hour and are serviced at an average rate of 15 cars per hour, with
service times exponential.
It is requested:
a) Probability that the system is empty.
b) Average number of clients in the washing system.
c) Average number of clients in the row.
d) Average time a customer waits in line.
e) Probability of having a row of more than 2 clients.
f) Probability of waiting...

The next four questions are based on the following information.
At a car wash station, on average, there are 4 cars coming in for
the service every 10 minutes. The average wash time is 2 minutes.
The Poisson distribution is appropriate for the arrival rate and
service times are exponentially distributed. Please convert all
rates into cars per hour and answer the following questions.
1.
The average time a car spent in the waiting line is ___________
hours, and the...

QUESTION 1
CC Car Wash specializes in car cleaning services. The services
offered by the company, the exact service time, and the resources
needed for each of them are described in the table following:
Service
Description
Processing Time
Resource
A. Wash
Exterior car washing and drying
10 minutes
1 automated washing machine
B. Wax
Exterior car waxing
15 minutes
1 automated waxing machine
C. Wheel Cleaning
Detailed cleaning of all wheels
16 minutes
1 employee
D. Interior Cleaning
Detailed cleaning...

QUESTION 1
CC Car Wash specializes in car cleaning services. The services
offered by the company, the exact service time, and the resources
needed for each of them are described in the table following:
Service
Description
Processing Time
Resource
A. Wash
Exterior car washing and drying
10 minutes
1 automated washing machine
B. Wax
Exterior car waxing
15 minutes
1 automated waxing machine
C. Wheel Cleaning
Detailed cleaning of all wheels
16 minutes
1 employee
D. Interior Cleaning
Detailed cleaning...

QUESTION 1
CC Car Wash specializes in car cleaning services. The services
offered by the company, the exact service time, and the resources
needed for each of them are described in the table following:
Service
Description
Processing Time
Resource
A. Wash
Exterior car washing and drying
10 minutes
1 automated washing machine
B. Wax
Exterior car waxing
15 minutes
1 automated waxing machine
C. Wheel Cleaning
Detailed cleaning of all wheels
16 minutes
1 employee
D. Interior Cleaning
Detailed cleaning...

1. Schmutz Auto Wash provides car washes. Its production
function is ? = 2?1/2(? - 1)1/2
where ? is cars washed per day, ? is daily hours of labor input,
and ? is daily usage of capital inputs. The price of a unit of
capital input is $48. The price of a unit of labor input is $16. In
the short run, Schmutz has one unit of capital input installed (so
? = 1).
a). Find Schmutz’s short run daily...

1. Summarize in a few sentences what Ayers found about pricing
strategies in car markets.
2. Do you think that this is a profit maximizing strategy? Do
you think this is an appropriate and reasonable strategy for
businesses to undertake it it increases their profits?
3. Can you think of other goods or services that could be - or
are - priced the same way? Check out the article on discrimination
in coffee shops "Waiting for Good Joe" for some...

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INNOVATION
Deep Change: How Operational Innovation Can Transform Your
Company
by
Michael Hammer
From the April 2004 Issue
Save
Share
8.95
In 1991, Progressive Insurance, an automobile insurer based in
Mayfield Village, Ohio, had approximately $1.3 billion in sales. By
2002, that figure had grown to $9.5 billion. What fashionable
strategies did Progressive employ to achieve sevenfold growth in
just over a decade? Was it positioned in a high-growth industry?
Hardly. Auto insurance is a mature, 100-year-old industry...

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