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Problem 1 A quick lube auto...

Problem 1

A quick lube auto service business wishes to simulate the arrival of vehicles for service. The manager has tracked and logged the number of vehicles arriving during the past 200 hours the business was open. She summarized the data in the following table.

Number of Cars Arriving Arrival Frequency

2 or less 0

3 20

4 30

5 50

6 60

7 40

8 0

a) Set up a table showing the probability and cumulative probability distribution for the vehicle arrival variable.

b) Establish random number intervals for the variable.

c) Simulate 12 hours of quick lube arrivals by using the random number table 14.4 on page 539 of your text. Start with the 3rd digit in the first column. It is 82.

d) What is the average number of arriving vehicles from part C of the problem?

Problem 2

A bakery near a large office complex sells boxes of pastries each morning primarily to the employees of the office complex. Because the bakery’s location is very near the office park, sales come from walk-in customers and there are very few preorders. A mix of pastries are baked and decorated throughout the night and boxed by 6 am and any unsold pastries at the end of the day are donated to a local food pantry. Pastries are only sold by the box and they have never sold fewer than 24 boxes or more than 28 boxes in a day. The number of walk-in customer purchases each day is shown in the following probability distribution.

Number of boxes sold Probability

24 .15

25 .22

26 .24

27 .21

28 .18

Each box of pastries costs $3.00 to make and is sold for $7.50.

a) Simulate the sales of boxed pastries for the next 10 business days using the last column in the random number table 14.4 in your text. Select the random number at the top of the last column as the first number.

b) If the bakery manager decides to schedule baking and boxing of 26 boxes for each of the 10 days, what would be the profits ( sales volume – costs) for the demand you simulated in part a?

c) If the bakery manager had decided to schedule 27 boxes instead of 25 boxes for each of the 10 days, what would be the profits for the demand you simulated in part a ?

d) EXTRA CREDIT question – 5 points Describe the relationship between the answers for part b and part c and what happened to cause this relationship.

Problem 3

A clothing boutique is considering hiring another sales associate to serve customers. The store owner has tracked the number of customers coming into the store in any 10 minute period. She has kept track of this information for 100, ten minute segments and developed the following data table along with the interval of random numbers.

Number of Arrivals

Probability

Interval of

Random Numbers

6

0.2

01-20

7

0.3

21-50

8

0.3

51-80

9

0.1

81-90

10

0.1

91-00

If you wanted to simulate the number of arrivals for the next three, ten minute intervals and chose the random numbers 18, 89 and 67, how many customers would be simulated to arrive in this 30 minute time period?

A quick lube auto service business wishes to simulate the arrival of vehicles for service. The manager has tracked and logged the number of vehicles arriving during the past 200 hours the business was open. She summarized the data in the following table.

Number of Cars Arriving Arrival Frequency

2 or less 0

3 20

4 30

5 50

6 60

7 40

8 0

a) Set up a table showing the probability and cumulative probability distribution for the vehicle arrival variable.

b) Establish random number intervals for the variable.

c) Simulate 12 hours of quick lube arrivals by using the random number table 14.4 on page 539 of your text. Start with the 3rd digit in the first column. It is 82.

d) What is the average number of arriving vehicles from part C of the problem?

Problem 2

A bakery near a large office complex sells boxes of pastries each morning primarily to the employees of the office complex. Because the bakery’s location is very near the office park, sales come from walk-in customers and there are very few preorders. A mix of pastries are baked and decorated throughout the night and boxed by 6 am and any unsold pastries at the end of the day are donated to a local food pantry. Pastries are only sold by the box and they have never sold fewer than 24 boxes or more than 28 boxes in a day. The number of walk-in customer purchases each day is shown in the following probability distribution.

Number of boxes sold Probability

24 .15

25 .22

26 .24

27 .21

28 .18

Each box of pastries costs $3.00 to make and is sold for $7.50.

a) Simulate the sales of boxed pastries for the next 10 business days using the last column in the random number table 14.4 in your text. Select the random number at the top of the last column as the first number.

b) If the bakery manager decides to schedule baking and boxing of 26 boxes for each of the 10 days, what would be the profits ( sales volume – costs) for the demand you simulated in part a?

c) If the bakery manager had decided to schedule 27 boxes instead of 25 boxes for each of the 10 days, what would be the profits for the demand you simulated in part a ?

d) EXTRA CREDIT question – 5 points Describe the relationship between the answers for part b and part c and what happened to cause this relationship.

Problem 3

A clothing boutique is considering hiring another sales associate to serve customers. The store owner has tracked the number of customers coming into the store in any 10 minute period. She has kept track of this information for 100, ten minute segments and developed the following data table along with the interval of random numbers.

Number of Arrivals

Probability

Interval of

Random Numbers

6

0.2

01-20

7

0.3

21-50

8

0.3

51-80

9

0.1

81-90

10

0.1

91-00

If you wanted to simulate the number of arrivals for the next three, ten minute intervals and chose the random numbers 18, 89 and 67, how many customers would be simulated to arrive in this 30 minute time period?

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