Waiting lines

User Generated

ZNAFGRE53

Business Finance

Description

attached the help sheets.

The actual problems needs to be complete are the attachment that say " Problems week 6"

Problems require that you use Excel QM, however some chapters will require you to use the Solver Add-In for Excel (regression) or simply type in formulas and make calculations. The answers must be submitted to D2L in a Microsoft Word or Microsoft Excel file.

You must state your answers within a complete sentence so that your understanding of applying the results of the computations can be observed. You should also include the work for your computation; this will assist in applying partial credit if your answers are

not correct.

the textbook:

Problems:

12 and 23. Using QM Excel.

39, 40, 41. Using QM Excel

Unformatted Attachment Preview

12. From historical data, Harry’s Car Wash estimates that dirty cars arrive at the rate of 10 per hour all day Saturday. With a crew working the wash line, Harry figures that cars can be cleaned at the rate of one every 5 minutes. One car at a time is cleaned in this example of a single-channel waiting line. Assuming Poisson arrivals and exponential service times, find the a. average number of cars in line. b. average time a car waits before it is washed. c. average time a car spends in the service system. d. utilization rate of the car wash. e. probability that no cars are in the system. 23. Bill First, general manager of Worthmore Department Store, has estimated that every hour of customer time spent waiting in line for a sales clerk to become available costs the store $100 in lost sales and goodwill. Customers arrive at the checkout counter at the rate of 30 per hour, and the average service time is 3 minutes. The Poisson distribution describes the arrivals, and the service times are exponentially distributed. The number of sales clerks can be 2, 3, or 4, with each one working at the same rate. Bill estimates the salary and benefits for each clerk to be $10 per hour. The store is open 10 hours per day. a. Find the average time in the line if 2, 3, and 4 clerks are used. b. What is the total time spent waiting in line each day if 2, 3, and 4 clerks are used? c. Calculate the total of the daily waiting cost and the daily service cost if 2, 3, and 4 clerks are used. What is the minimum total daily cost? 39 Grey Construction would like to determine the least expensive way of connecting houses it is building with cable TV. It has identified 11 possible branches or routes that could be used to connect the houses. The cost in hundreds of dollars and the branches are summarized in the following table. a. What is the least expensive way to run cable to the houses? BRANCH START NODE END NODE COST ($100s) Branch 1 1 2 5 Branch 2 1 3 6 Branch 3 1 4 6 Branch 4 1 5 5 Branch 5 2 6 7 Branch 6 3 7 5 Branch 7 4 7 7 Branch 8 5 8 4 Branch 9 6 7 1 Branch 10 7 9 6 Branch 11 8 9 2 b. After reviewing cable and installation costs, Grey Construction would like to alter the costs for installing cable TV between its houses. The first branches need to be changed. The changes are summarized in the following table. What is the impact on total costs? BRANCH START NODE END NODE COST ($100s) Branch 1 1 2 5 Branch 2 1 3 1 Branch 3 1 4 1 Branch 4 1 5 1 Branch 5 2 6 7 Branch 6 3 7 5 Branch 7 4 7 7 Branch 8 5 8 4 Branch 9 6 7 1 Branch 10 7 9 6 Branch 11 8 9 2 40. In going from Quincy to Old Bainbridge, there are 10 possible roads that George Olin can take. Each road can be considered a branch in the shortest-route problem. a. Using the following table, determine the route from Quincy (node 1) to Old Bainbridge (node 8) that will minimize total distance traveled. All distances are in hundreds of miles. BRANCH START NODE END NODE DISTANCE (100s OF MILES) Branch 1 1 2 3 Branch 2 1 3 2 Branch 3 2 4 3 Branch 4 3 5 3 Branch 5 4 5 1 Branch 6 4 6 4 Branch 7 5 7 2 Branch 8 6 7 2 Branch 9 6 8 3 Branch 10 7 8 6 b. George Olin made a mistake in estimating the distances from Quincy to Old Bainbridge. The new distances are given in the following table. What impact does this have on the shortest route from Quincy to Old Bainbridge? BRANCH START NODE END NODE DISTANCE (100s OF MILES) Branch 1 1 2 3 Branch 2 1 3 2 Branch 3 2 4 3 Branch 4 3 5 1 Branch 5 4 5 1 Branch 6 4 6 4 Branch 7 5 7 2 Branch 8 6 7 2 Branch 9 6 8 3 Branch 10 7 8 6 41. South Side Oil and Gas, a new venture in Texas, has developed an oil pipeline network to transport oil from exploration fields to the refinery and other locations. There are 10 pipelines (branches) in the network. The oil flow in hundreds of gallons and the network of pipelines are given in the following table. a. What is the maximum that can flow through the network? BRANCH START END NODE NODE Branch 1 1 2 10 4 10 Branch 2 1 3 8 2 5 Branch 3 2 4 12 1 10 Branch 4 2 5 6 6 0 Branch 5 3 5 8 1 5 Branch 6 4 6 10 2 10 Branch 7 5 6 10 10 0 Branch 8 5 7 5 5 5 Branch 9 6 8 10 1 10 Branch 7 8 10 1 5 10 CAPACITY REVERSE FLOW CAPACITY b. South Side Oil and Gas needs to modify its pipe-line network flow patterns. The new data are given in the following table. What impact does this have on the maximum flow through the network? BRANCH START END NODE NODE Branch 1 1 2 10 4 10 Branch 2 1 3 8 2 5 Branch 3 2 4 12 1 10 Branch 4 2 5 0 0 0 Branch 5 3 5 8 1 5 Branch 6 4 6 10 2 10 Branch 7 5 6 10 10 0 Branch 8 5 7 5 5 5 Branch 9 6 8 10 1 10 Branch 7 8 10 1 5 10 CAPACITY REVERSE FLOW CAPACITY
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Explanation & Answer

Hello there,As promised to you I finished your task. I am attaching to this message a Microsoft Word file entitled " Final version for Management Analysis " which contains your step by step guide and also a Microsoft Excel file entitled " Nodes Excel" which contains the excel problems (they are also available in the word file).There were a total of 5 problems: 12, 23, 39, 40, 41What is written in bold in the word file is the task's textWhat is in italic is the answer (step by step)What is highlighted in yellow is either a very important value or a final answerWhat is written in tables is a formula I applied.The last page contains a step by step guide on how to solve similar problem ( explaining each step and made several print screens for a better understanding)---The normal format didn't bother to put it in APA because I suppose you don't need it. All the steps of how I reached the answers are included.Number of pages: 24---Please take a look and tell me if this is what you needed (which i suppose it is haha)

A

B

C

D

E

F

G

H

I

J

K

1
2
3

Grey Construction

4
5

Least expensive

6
7
8
9
10 Data -Price Table
11 From\to

Node 1

Node 2

Node 3

Node 4

Node 5

Node 6

Node 7

Node 8

Node 9

12 Node 1

0

5

6

6

5

0

0

0

0

13 Node 2

0

0

0

0

0

7

0

0

0

14 Node 3

0

0

0

0

0

0

5

0

0

15 Node 4

0
0
0
0
0

0
0
0
0
0

0
0
0
0
0

0
0
0
0
0

0
0
0
0
0

0
0
0
0
0

7
0
1
0
0

0
4
0
0
0

0
0
0
6
2

16
17
18
19

Node 5
Node 6
Node 7
Node 8

A

B

20 Node 9
21
22 Start=1,Finish=-1
23
24 Flows
25
26
27
28
29
30
31
32
33
34

Node 1
Node 2
Node 3
Node 4
Node 5
Node 6
Node 7
Node 8
Node 9
35 Inflow
36 Outflow
37 Net Outflow
38
39 Minimum distance

From\to

C

D

E

F

G

H

I

J

K

0
1

0
0

0
0

0
0

0
0

0
0

0
0

0
0

0
-1

Node 1

Node 2

Node 3

Node 4

Node 5
1

Node 6

Node 7

Node 8

Node 9

1

1

1

1
1
11

1
1

1
1

Outflow
1

1
-1

1

L

M

N

O

P

Q

R

START
NODE

END
NODE

COST
($100s)

1

2

5

1

3

6

1

4

6

1

5

5

2

6

7

3

7

5

4

7

7

5

8

4

6

7

1

7

9

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9

2

1
2
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4
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8
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19

Data problem
BRAN
CH
Branch
1
Branch
2
Branch
3
Branch
4
Branch
5
Branch
6
Branch
7
Branch
8
Branch
9
Branch
10
Branch
11

A

B

C

D

E

F

G

H

I

J

K

1
2
3

BGrey Construction

4
5

Least expensive

6

7
8
9
10 Data - Price Table
11 From\to

Node 1

Node 2

Node 3

Node 4

Node 5

Node 6

Node 7

Node 8

Node 9

12 Node 1

0

5

1

1

1

0

0

0

0

13 Node 2

0

0

0

0

0

7

0

0

0

14 Node 3

0

0

0

0

0

0

5

0

0

15 Node 4

0

0

0

0

0

0

7

0

0

16 Node 5

0

0

0

0

0

0

0

4

0

17 Node 6

0

0

0

0

0

0

1

0

0

18 Node 7

0
0

0
0

0
0

0
0

0
0

0
0

0
0

0
0

6
2

19 Node 8

A

B

20 Node 9
21
22 Start=1,Finish=-1
23
24 Flows
25
26
27
28
29
30
31
32
33
34

From\to

C

D

E

F

G

H

I

J

K

0
1

0
0

0
0

0
0

0
0

0
0

0
0

0
0

0
-1

Node 1

Node 2

Node 3

Node 4

Node 5
1

Node 6

Node 7

Node 8

Node 9

Node 1
Node 2
Node 3
Node 4
Node 5
Node 6
Node 7
Node 8
Node 9
35 Inflow
36 Outflow
37 Net Outflow

1
1

38
39 Minimum distance

7

1

1

1
1
1

1
1

Outflow
1

1
-1

1

L

M

N

O

P

Q

R

START
NODE

END
NODE

COST
($100s)

1

2

5

1

3

1

1

4

1

1

5

1

2

6

7

3

7

5

4

7

7

5

8

4

6

7

1

7

9

6

8

9

2

1
2
3
4
5
6

7
8
9
10
11
12
13
14
15
16
17
18
19

Problem Data
BRAN
CH
Branch
1
Branch
2
Branch
3
Branch
4
Branch
5
Branch
6
Branch
7
Branch
8
Branch
9
Branch
10
Branch
11

A

B

C

D

E

F

G

H

I

J

1
2
3

AQuincy to Old Bainbridge

4

5

Shortest Path

6
7
8
9
10 Data - Distance Table
11 From\to

Nodes 1

Nodes 2

Nodes 3

Nodes 4

Nodes 5

Nodes 6

Nodes 7

Nodes 8

12 Nodes 1

0

3

2

0

0

0

0

0

13 Nodes 2

0

0

0

3

0

0

0

0

14 Nodes 3

0

0

0

0

3

0

0

0

15 Nodes 4

0
0
0

0
0
0

0
0
0

0
0
0

1
0
0

4
0
0

0
2
2

0
0
3

16 Nodes 5
17 Nodes 6

A
18
19
20
21
22
23

B

Nodes 7
Nodes 8

C

D

E

F

G

H

I

J

0
0
1

0
0
0

0
0
0

0
0
0

0
0
0

0
0
0

0
0
0

6
0
-1

Nodes 1

Nodes 2
1

Nodes 3

Nodes 4

Nodes 5

Nodes 6

Nodes 7

Nodes 8

Start=1,Finish=-1
Flows

24
25
26
27
28
29
30
31
32

Nodes 1
Nodes 2
Nodes 3
Nodes 4
Nodes 5
Nodes 6
Nodes 7
Nodes 8
33 Inflow
34 Outflow
35 Net Outflow
36
37 Minimum distance

From\to

1
1

1
1

1
1
13

1
1

1
1

1
1

Outflow
1
1

1
-1

1

K

L

M

N

O

P

START
NODE

END
NODE

D...


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