assigment 2 - total project cost

7/30/2019 Assigment 2 - Total Project Cost

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NATIONAL TAIWAN UNIVERSITY OF SCIENCE AND TECHNOLOGY

DEPARTMENT OF CONSTRUCTION ENGINEERING

Course

COST MANAGEMENT

- ASSIGNMENT 2 -

Total Project Cost

by Monte Carlo Simulation

Instructor: Professor J.-S. Chou

Student: Ung Thanh KhietM10105813

Taipei, April - 2013


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TABLE OF CONTENT

1. Assuming data of project cost items ........................................................................ 2

2. Simulation for TPC .................................................................................................. 3

2.1. Correlation r=0.3............................................................................................. 3

2.2. Correlation r=0................................................................................................ 4

2.3. Correlation r = -0.3 ......................................................................................... 5

3.

Comparing TPCs PDF and CPF ............................................................................. 7

4. Simulating the problem by using sofware CRYSTAL BALL ................................ 9

5. Appendix ................................................................................................................ 12


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Problem:

1. Assume 7 work items with its distribution as normal, lognormal and triangular.The total cost of project (TPC) y:

7

1

i

i

y x

2. To conduct simulation for TPC if all cost components are correlated withcoefficient r1= 0.3; r2 = 0 and r3= -0.3 respectively.

Simulation 50 times with 20 sets

3. Draw TPCs PDF and CPF and discussing your results.4. Simulating the problem by using sofware (Crystal Ball or @Risk) and

comparing the result from manual spread and from software.

Solution:

1. Assuming data of project cost itemsIt is considered a high-rise building project with below basic information about

main items and cost distribution.

Table 1: Project cost items

Distribution:

- Normal distribution: the CDF is given byk k

X

X

X F (x)

- Lognormal distribution: the CDF is given by


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X

ln xF x

- Triangular distribution:

The inverse of F(x) as follows:

1

m a: 0 ya y* m a (b a) b a

F ( y |a,m,b,n)m a

b 1 y b m b a : y 1b a

for

for

2. Simulation for TPC2.1.Correlation r=0.3- Matrix of r value

1 2 3 4 5 6 7

Matrix of r 1 1.00 0.30 0.30 0.30 0.30 0.30 0.30

2 0.30 1.00 0.30 0.30 0.30 0.30 0.303 0.30 0.30 1.00 0.30 0.30 0.30 0.30

4 0.30 0.30 0.30 1.00 0.30 0.30 0.30

5 0.30 0.30 0.30 0.30 1.00 0.30 0.30

6 0.30 0.30 0.30 0.30 0.30 1.00 0.30

7 0.30 0.30 0.30 0.30 0.30 0.30 1.00

- C (Covariance matrix)1 2 3 4 5 6 7

Matrix C 1 52.56 18.04 11.26 10.60 10.77 16.19 42.59

2 18.04 68.81 12.89 12.13 12.32 18.52 48.72

3 11.26 12.89 26.81 7.57 7.69 11.56 30.42

4 10.60 12.13 7.57 23.77 7.24 10.88 28.64

5 10.77 12.32 7.69 7.24 24.50 11.05 29.07

6 16.19 18.52 11.56 10.88 11.05 55.38 43.71

7 42.59 48.72 30.42 28.64 29.07 43.71 383.38

- Tranformation matrix A is obtained as follows:

12

1,

i

ii ijja COV Xi Xi a


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1

1,

i

i j ih jhhij

ii

COV X X a aa

a

1 2 3 4 5 6 7

Matrix A 1 7.25 0.00 0.00 0.00 0.00 0.00 0.002 2.49 7.91 0.00 0.00 0.00 0.00 0.00

3 1.55 1.14 4.81 0.00 0.00 0.00 0.00

4 1.46 1.07 0.85 4.44 0.00 0.00 0.00

5 1.48 1.09 0.86 0.71 4.46 0.00 0.00

6 2.23 1.64 1.30 1.07 0.91 6.64 0.00

7 5.87 4.31 3.41 2.82 2.40 2.10 17.34

- Matrix A can be checked as:'

T

X XC AC A

1 2 3 4 5 6 7

Check A 1 52.56 18.04 11.26 10.60 10.77 16.19 42.59

2 18.04 68.81 12.89 12.13 12.32 18.52 48.72

3 11.26 12.89 26.81 7.57 7.69 11.56 30.42

4 10.60 12.13 7.57 23.77 7.24 10.88 28.64

5 10.77 12.32 7.69 7.24 24.50 11.05 29.07

6 16.19 18.52 11.56 10.88 11.05 55.38 43.71

7 42.59 48.72 30.42 28.64 29.07 43.71 383.38

Run simulation with 50 realizations. See Appendix 1.

2.2.Correlation r=01 2 3 4 5 6 7

Matrix of 1 1.00 0.00 0.00 0.00 0.00 0.00 0.00

2 0.00 1.00 0.00 0.00 0.00 0.00 0.00

3 0.00 0.00 1.00 0.00 0.00 0.00 0.00

4 0.00 0.00 0.00 1.00 0.00 0.00 0.00

5 0.00 0.00 0.00 0.00 1.00 0.00 0.00

6 0.00 0.00 0.00 0.00 0.00 1.00 0.00

7 0.00 0.00 0.00 0.00 0.00 0.00 1.00

1 2 3 4 5 6 7

Matrix C 1 52.56 0.00 0.00 0.00 0.00 0.00 0.00

2 0.00 68.81 0.00 0.00 0.00 0.00 0.00

3 0.00 0.00 26.81 0.00 0.00 0.00 0.00

4 0.00 0.00 0.00 23.77 0.00 0.00 0.00

5 0.00 0.00 0.00 0.00 24.50 0.00 0.00

6 0.00 0.00 0.00 0.00 0.00 55.38 0.00

7 0.00 0.00 0.00 0.00 0.00 0.00 383.38


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1 2 3 4 5 6 7

Matrix A 1 7.25 0.00 0.00 0.00 0.00 0.00 0.00

2 0.00 8.30 0.00 0.00 0.00 0.00 0.00

3 0.00 0.00 5.18 0.00 0.00 0.00 0.00

4 0.00 0.00 0.00 4.88 0.00 0.00 0.00

5 0.00 0.00 0.00 0.00 4.95 0.00 0.00

6 0.00 0.00 0.00 0.00 0.00 7.44 0.00

7 0.00 0.00 0.00 0.00 0.00 0.00 19.58

1 2 3 4 5 6 7

Check A 1 52.56 0.00 0.00 0.00 0.00 0.00 0.00

2 0.00 68.81 0.00 0.00 0.00 0.00 0.00

3 0.00 0.00 26.81 0.00 0.00 0.00 0.00

4 0.00 0.00 0.00 23.77 0.00 0.00 0.00

5 0.00 0.00 0.00 0.00 24.50 0.00 0.00

6 0.00 0.00 0.00 0.00 0.00 55.38 0.007 0.00 0.00 0.00 0.00 0.00 0.00 383.38


2.3.Correlation r = -0.3- With r = 0.3, we calculate tTranformation matrix A:

1 2 3 4 5 6 7

Matrix A 1 7.25 0.00 0.00 0.00 0.00 0.00 0.00

2 -2.49 7.91 0.00 0.00 0.00 0.00 0.003 -1.55 -2.12 4.46 0.00 0.00 0.00 0.00

4 -1.46 -1.99 -3.15 2.78 0.00 0.00 0.00

5 -1.48 -2.02 -3.20 -8.47 #NUM! 0.00 0.00

6 -2.23 -3.04 -4.81 -12.73 #NUM! #NUM! 0.00

7 -5.87 -8.00 -12.66 -33.49 #NUM! #NUM! #NUM!

We occured this error#NUM! because the equation: 1

2

1

,i

ii ij

j

a COV Xi Xi a

with value under square root is less than zero.

To compare the results of three neutral, positive and negative correlation cases, I

would like to propose the new negative coefficient r = -0.15.


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r = -0.15

1 2 3 4 5 6 7

Matrix of r 1 1.00 -0.15 -0.15 -0.15 -0.15 -0.15 -0.15

2 -0.15 1.00 -0.15 -0.15 -0.15 -0.15 -0.15

3 -0.15 -0.15 1.00 -0.15 -0.15 -0.15 -0.15

4 -0.15 -0.15 -0.15 1.00 -0.15 -0.15 -0.15

5 -0.15 -0.15 -0.15 -0.15 1.00 -0.15 -0.15

6 -0.15 -0.15 -0.15 -0.15 -0.15 1.00 -0.15

7 -0.15 -0.15 -0.15 -0.15 -0.15 -0.15 1.00

1 2 3 4 5 6 7

Matrix C 1 52.56 -9.02 -5.63 -5.30 -5.38 -8.09 -21.29

2 -9.02 68.81 -6.44 -6.07 -6.16 -9.26 -24.36

3 -5.63 -6.44 26.81 -3.79 -3.84 -5.78 -15.21

4 -5.30 -6.07 -3.79 23.77 -3.62 -5.44 -14.325 -5.38 -6.16 -3.84 -3.62 24.50 -5.53 -14.54

6 -8.09 -9.26 -5.78 -5.44 -5.53 55.38 -21.86

7 -21.29 -24.36 -15.21 -14.32 -14.54 -21.86 383.38

1 2 3 4 5 6 7

Matrix A 1 7.25 0.00 0.00 0.00 0.00 0.00 0.00

2 -1.24 8.20 0.00 0.00 0.00 0.00 0.00

3 -0.78 -0.90 5.04 0.00 0.00 0.00 0.00

4 -0.73 -0.85 -1.02 4.63 0.00 0.00 0.00

5 -0.74 -0.86 -1.03 -1.28 4.53 0.00 0.00

6 -1.12 -1.30 -1.55 -1.93 -2.55 6.31 0.00

7 -2.94 -3.42 -4.08 -5.08 -6.71 -9.96 13.28

1 2 3 4 5 6 7

Check A 1 52.56 -9.02 -5.63 -5.30 -5.38 -8.09 -21.29

2 -9.02 68.81 -6.44 -6.07 -6.16 -9.26 -24.36

3 -5.63 -6.44 26.81 -3.79 -3.84 -5.78 -15.21

4 -5.30 -6.07 -3.79 23.77 -3.62 -5.44 -14.32

5 -5.38 -6.16 -3.84 -3.62 24.50 -5.53 -14.54

6 -8.09 -9.26 -5.78 -5.44 -5.53 55.38 -21.86

7 -21.29 -24.36 -15.21 -14.32 -14.54 -21.86 383.38



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The result of TPC with 50 times and 20 sets as follows:

Sim. Set r = 0.3 r=0 r = -0.15

1 501.04 503.87 503.39

2 499.61 500.09 504.09

3 506.57 501.83 500.27

4 501.04 499.44 500.67

5 503.14 499.67 502.84

6 506.30 502.70 503.40

7 507.94 503.60 498.12

8 497.74 500.73 503.62

9 501.46 500.01 507.48

10 500.82 505.88 508.07

11 500.29 502.70 501.32

12 510.95 507.83 503.92

13 511.08 504.64 504.7614 502.83 506.73 500.52

15 501.70 503.16 506.85

16 497.91 505.13 501.51

17 500.01 512.32 504.08

18 514.80 501.19 502.01

19 506.27 504.79 503.79

20 502.14 508.42 503.74

Mean 503.68 503.74 503.22

Standard Deviation 4.68 3.35 2.48

Standard Error 0.15 0.11 0.08

Minimum 497.74 499.44 498.12

Maximum 514.80 512.32 508.07

Lower 95% 503.44 503.56 503.09

Upper 95% 503.93 503.91 503.35

3. Comparing TPCs PDF and CPF


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When we simulate TPC with 50 times and 20 sets, result is showed as follow:

E (TPC) 503.45

Var (TPC) 1,438.93

s (TPC) 37.93

Assume TPC is Normal

Dicussion:

In positive correlation condition r = 0.3, the result we got after simulating for total

cost is different from independent result because the standard deviation is greater than

the standard of the first case.

In negative correlation condition r = -0.15, the result we got after simulating for

total cost is different from independent result because the standard deviation is smaller

than the standard of the first case.

Three scenarios show three levels of risk prefer status, the lowest risk seeker or

risk averse in case of correlation coefficient r = 0.3 and the highest risk seeker or risk

averse in case of correlation coefficient r = -0.15

Based on risk assessment, in case of correlation condition r = 0.3, the CDF line islowest, that mean it will be got more uncertainty for decision maker. However, in

positive risk aspect, decision maker have a trend seek risk to gain more benefit than

original plan, and otherwise.


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4. Simulating the problem by using sofware CRYSTAL BALLUsing software step by step:

- Defining distribution of items:

- Defining correlation matrix:

- Defining Forecast cell:


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- Set Run preferences, set number of trials run to 50

- Run and get the resultr = 0.3

From Crystal Ball From manual spread

r = 0



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r = - 0.15


Comment:The two results from Crystal Ball look similiar. But the chart from CB are smoother.

And, clearly, using CB is quicker, more efficiently.


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5. AppendixAPPENDIX 1: Simulation case r = 0.3

502.95

Min-M Mid-M TPC

1 0.936 -0.665 1.442 0.382 -0.206 -1.531 -1.588 64.32 84.85 52.46 68.68 54.26 63.80 101.71 64.20 84.52 52.77 68.58 54.70 54.71 54.70 63.80 101.71 490.29

2 -1.296 0.068 -0.081 1.157 0.335 0.335 0.385 48.15 85.09 42.51 68.35 53.40 71.76 128.18 48.52 84.76 42.30 68.24 53.84 53.95 53.84 71.76 128.18 497.59

3 -0.120 1.173 1.992 -0.352 -0.810 1.027 -1.731 56.67 96.76 55.56 66.31 51.96 80.81 104.66 56.23 96.78 56.53 66.13 52.24 52.77 52.24 80.81 104.66 513.39

4 -0.767 -1.028 1.060 1.488 -1.180 -1.901 0.216 51.98 77.74 47.57 70.39 47.45 56.75 120.12 51.85 77.96 47.33 70.40 46.87 50.30 46.87 56.75 120.12 471.29

5 0.272 0.973 0.009 1.853 -0.442 -0.095 0.728 59.51 96.16 46.41 74.79 53.82 74.03 146.72 59.07 96.12 46.12 75.32 54.27 54.32 54.27 74.03 146.72 551.66

6 -2.801 0.735 -2.450 -0.065 0.630 1.247 -0.373 37.23 86.62 29.55 59.42 50.29 71.43 100.16 40.17 86.25 31.71 59.50 50.26 51.63 50.26 71.43 100.16 439.47

7 -1.032 1.243 2.306 1.046 0.541 -0.279 0.042 50.06 95.05 55.73 71.53 57.96 73.36 135.86 50.15 94.92 56.75 71.65 57.41 58.16 58.16 73.36 135.86 540.85

8 -0.560 -0.580 1.383 -0.022 3.058 -0.051 -0.841 53.48 81.80 49.95 64.73 66.34 72.90 115.85 53.21 81.65 49.90 64.56 58.94 63.13 63.13 72.90 115.85 501.20

9 -0.097 0.948 -1.590 1.678 0.993 -1.053 -0.499 56.84 95.04 38.12 72.09 58.14 65.87 118.67 56.40 94.90 38.37 72.26 57.50 58.31 58.31 65.87 118.67 504.78

10 -1.689 1.693 -0.578 0.689 -0.201 -1.137 0.603 45.30 96.98 41.36 67.02 51.43 62.14 129.26 46.19 97.02 41.23 66.86 51.63 52.39 51.63 62.14 129.26 494.33

11 -0.161 0.929 0.435 0.623 -1.171 -1.047 -0.076 56.37 94.73 47.73 69.00 49.37 65.25 124.29 55.94 94.57 47.50 68.92 49.14 51.12 49.14 65.25 124.29 505.61

12 0.762 2.240 -1.108 -0.222 -0.027 0.007 1.771 63.07 107.40 43.25 66.69 55.34 74.60 164.71 62.82 109.23 42.99 66.52 55.66 55.71 55.71 74.60 164.71 576.58

13 -1.620 -0.377 -0.162 -1.165 -2.752 0.025 -1.455 45.80 80.77 41.11 57.01 36.95 62.84 77.56 46.59 80.69 41.00 57.34 40.46 49.31 40.46 62.84 77.56 406.48

14 0.669 0.589 -0.865 0.924 -1.213 -0.593 -0.511 62.39 94.10 42.39 70.08 49.14 68.16 117.44 62.09 93.90 42.18 70.08 48.86 51.00 48.86 68.16 117.44 502.70

15 0.946 0.038 0.922 1.596 2.763 0.258 -0.765 64.40 90.43 50.78 74.40 68.69 80.19 131.61 64.29 90.07 50.83 74.88 58.97 63.59 63.59 80.19 131.61 555.46

16 2.146 -0.875 -1.553 0.101 -0.843 0.582 -2.171 73.10 86.20 39.71 66.43 50.21 75.42 89.70 74.74 85.83 39.74 66.26 50.16 51.59 50.16 75.42 89.70 481.85

17 0.002 -0.561 -0.895 0.387 -0.020 -0.287 0.840 57.55 83.35 39.89 65.46 51.81 67.29 133.87 57.10 83.09 39.91 65.28 52.07 52.66 52.07 67.29 133.87 498.62

18 -0.858 -0.447 1.117 -0.827 -0.919 0.365 -1.393 51.32 82.11 48.36 60.64 47.52 70.37 93.23 51.26 81.94 48.17 60.62 46.95 50.32 46.95 70.37 93.23 452.54

19 1.718 0.172 -0.418 -1.297 -0.333 -0.347 0.353 70.00 93.42 45.69 61.68 52.97 70.45 134.67 70.83 93.17 45.39 61.60 53.38 53.58 53.38 70.45 134.67 529.50

20 -0.701 0.184 0.126 0.394 0.151 1.086 -0.344 52.46 87.49 44.56 66.13 53.22 77.54 119.21 52.28 87.10 44.27 65.95 53.66 53.80 53.66 77.54 119.21 500.01

21 1.812 0.735 -0.200 -0.027 -1.447 -1.199 -0.818 70.67 98.11 47.53 68.25 49.85 66.56 117.21 71.66 98.27 47.29 68.13 49.72 51.38 49.72 66.56 117.21 518.84

22 -0.138 0.772 0.675 0.726 -0.020 0.727 -0.716 56.54 93.54 48.74 69.52 54.65 78.29 120.25 56.11 93.31 48.58 69.48 55.06 55.06 55.06 78.29 120.25 521.07

23 0.509 0.317 2.644 0.473 0.535 -1.674 0.719 61.23 91.55 58.70 70.53 59.10 65.84 149.26 60.85 91.22 60.61 70.56 57.91 59.15 59.15 65.84 149.26 557.50

24 0.153 0.245 1.753 1.357 -2.689 -0.132 1.298 58.65 90.10 53.78 73.11 43.99 72.01 151.84 58.20 89.73 54.33 73.40 43.52 49.56 43.52 72.01 151.84 543.03

x2s1 s2 s3 s4 s5 s6 x'5# x'6 x'7 x1s7 x'1 x'2 x'3 x'4x5

x5 x6 x7x3 x4


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25 -2.057 0.243 -1.874 -2.081 -0.936 0.580 1.462 42.63 84.59 32.91 51.52 42.95 65.02 125.35 44.10 84.28 34.17 52.71 42.76 49.46 42.76 65.02 125.35 448.38

26 -1.636 0.128 -0.702 1.351 -0.081 0.102 -1.215 45.68 84.72 39.06 68.26 50.71 68.57 95.63 46.49 84.41 39.18 68.14 50.76 51.89 50.76 68.57 95.63 453.17

27 0.479 -0.101 -2.041 -1.219 -2.501 -0.070 1.848 61.01 88.17 35.65 58.54 39.83 65.08 142.19 60.63 87.78 36.31 58.70 41.18 49.33 41.18 65.08 142.19 491.88

28 0.050 0.006 1.250 1.172 -1.895 0.581 -1.744 57.90 87.95 50.93 71.45 46.55 76.00 98.64 57.45 87.56 51.00 71.56 45.89 50.03 45.89 76.00 98.64 488.10

29 -0.814 -1.040 -0.644 0.841 -0.355 0.857 -0.541 51.64 77.52 39.29 65.98 49.12 72.78 106.79 51.54 77.78 39.37 65.80 48.83 50.99 48.83 72.78 106.79 462.91

30 0.233 -0.170 0.744 0.145 0.439 0.470 0.227 59.23 87.01 48.58 66.53 55.86 75.76 133.88 58.78 86.63 48.40 66.36 56.08 56.20 56.20 75.76 133.88 526.02

31 -1.394 -0.790 -0.396 -1.087 -0.888 0.059 1.529 47.43 78.06 39.87 57.05 45.00 64.37 132.82 47.93 78.25 39.88 57.37 44.36 49.70 44.36 64.37 132.82 464.98

32 0.414 0.631 -0.824 -0.317 -0.731 0.157 1.152 60.54 93.81 42.24 64.28 50.11 71.80 144.31 60.13 93.59 42.04 64.10 50.03 51.53 50.03 71.80 144.31 526.01

33 -0.120 -1.571 -1.708 0.566 0.378 1.274 0.705 56.67 75.05 34.65 64.31 51.73 75.23 128.42 56.24 75.62 35.52 64.13 51.98 52.60 51.98 75.23 128.42 487.13

34 -0.089 0.936 0.977 -1.403 -0.889 0.482 -1.514 56.90 94.97 50.46 60.57 49.77 74.36 99.83 56.46 94.83 50.47 60.56 49.62 51.33 49.62 74.36 99.83 486.13

35 -1.183 -1.131 1.723 0.643 -1.624 -0.535 0.952 48.96 75.89 49.99 66.48 44.72 64.27 131.67 49.21 76.34 49.95 66.31 44.12 49.65 44.12 64.27 131.67 481.86

36 0.135 -0.056 -0.582 0.722 2.665 1.091 -0.720 58.52 87.68 42.19 67.95 65.03 80.78 121.13 58.06 87.29 41.99 67.82 58.90 62.72 62.72 80.78 121.13 519.79

37 -0.741 0.254 -0.077 -1.399 -0.217 0.895 0.396 52.17 87.94 43.60 58.00 50.14 73.78 125.07 52.02 87.55 43.33 58.22 50.07 51.55 50.07 73.78 125.07 490.05

38 -0.516 1.560 -0.364 1.171 -1.015 0.510 2.545 53.80 98.84 44.06 70.91 49.93 75.52 172.82 53.51 99.09 43.78 70.97 49.81 51.42 49.81 75.52 172.82 565.51

39 0.837 -0.400 -0.180 -0.898 -0.976 2.094 0.698 63.61 86.70 44.82 61.75 48.66 83.90 138.52 63.41 86.32 44.52 61.67 48.28 50.78 48.28 83.90 138.52 526.62

40 -0.654 -0.462 -0.290 0.295 -0.128 0.146 -0.465 52.80 82.50 41.90 64.71 50.91 69.45 110.28 52.59 82.30 41.73 64.54 51.01 52.03 51.01 69.45 110.28 471.88

41 -0.815 1.031 -1.744 0.962 1.020 1.425 0.405 51.63 93.91 36.36 67.81 56.64 79.91 133.21 51.54 93.70 36.89 67.68 56.64 56.94 56.94 79.91 133.21 519.87

42 -0.423 1.604 0.818 -0.900 -2.018 0.416 0.000 54.47 99.42 49.94 62.90 45.19 73.57 125.02 54.14 99.75 49.89 62.76 44.54 49.73 44.54 73.57 125.02 509.67

43 -0.417 1.049 0.193 0.371 -1.055 0.003 -0.309 54.52 95.04 46.31 67.43 49.25 71.36 120.20 54.18 94.91 46.03 67.28 48.99 51.06 48.99 71.36 120.20 502.96

44 0.496 -0.274 1.274 -0.820 -0.031 -0.183 -1.632 61.14 86.85 51.42 62.97 53.81 71.06 99.33 60.76 86.47 51.55 62.83 54.26 54.31 54.26 71.06 99.33 486.26

45 0.820 -1.306 -0.243 -0.324 -0.626 -0.006 0.456 63.48 79.48 43.45 63.25 49.57 69.29 128.15 63.27 79.53 43.19 63.10 49.37 51.22 49.37 69.29 128.15495.91

46 -0.382 -0.754 0.434 -0.799 1.189 0.482 -0.026 54.77 80.86 45.47 60.55 56.71 72.78 121.47 54.42 80.78 45.17 60.54 56.69 57.00 57.00 72.78 121.47 492.16

47 2.191 -0.408 0.058 -0.107 -1.427 0.800 1.011 73.43 90.00 48.05 67.44 49.42 79.07 151.11 75.16 89.63 47.84 67.29 49.20 51.15 49.20 79.07 151.11 559.30

48 0.799 1.156 -0.329 0.041 -0.243 0.431 0.550 63.33 98.92 45.81 67.41 54.11 76.81 142.85 63.11 99.18 45.52 67.26 54.56 54.57 54.56 76.81 142.85 549.30

49 0.230 -0.100 -0.415 -0.771 -0.096 0.227 -0.808 59.21 87.56 43.08 61.55 51.90 71.28 107.89 58.76 87.18 42.84 61.48 52.17 52.73 52.17 71.28 107.89 481.59

50 0.190 0.383 0.627 -0.509 -0.860 -2.125 0.885 58.92 91.29 48.58 64.06 50.04 57.31 136.61 58.47 90.94 48.41 63.89 49.95 51.49 49.95 57.31 136.61 505.58


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Page 14

APPENDIX 2: Simulation case r = 0

503.49

Min-Mid Mid-Max TPC

1 -0.278 0.357 -0.371 0.454 0.136 -1.495 -2.125 55.52 90.74 42.91 67.31 53.67 59.75 82.71 55.13 90.38 42.68 67.16 5 4.1 2 5 4.1 8 54.12 59.75 82.71 451.93

2 -1.117 1.250 1.019 0.610 0.985 0.558 1.673 49.44 98.15 50.11 68.08 57.87 75.03 157.07 49.62 98.32 50.08 67.95 5 7.3 6 5 8.0 8 58.08 75.03 157.07 556.15

3 -0.066 -1.644 -1.302 -0.679 0.543 -1.082 -0.097 57.06 74.14 38.09 61.79 55.69 62.82 122.41 56.62 74.84 38.34 61.71 5 5.9 5 5 6.0 4 56.04 62.82 122.41 472.78

4 -0.735 -0.820 -0.503 -1.093 1.623 -0.296 -0.303 52.21 80.98 42.23 59.77 61.04 68.67 118.38 52.06 80.89 42.03 59.82 5 8.4 7 6 0.6 4 60.64 68.67 118.38 482.50

5 0.006 1.176 0.480 0.766 -0.211 0.502 -0.965 57.59 97.53 47.32 68.83 51.96 74.61 105.42 57.13 97.64 47.07 68.74 5 2.2 5 5 2.7 7 52.25 74.61 105.42 502.86

6 -2.097 -1.749 -0.341 -0.710 1.347 -0.646 0.669 42.34 73.27 43.07 61.64 59.67 66.07 137.43 43.88 74.11 42.82 61.56 5 8.1 1 5 9.6 2 59.62 66.07 137.43 485.48

7 -0.975 -0.829 0.065 0.422 -0.192 2.084 0.422 50.47 80.90 45.17 67.16 52.05 86.38 132.58 50.52 80.82 44.88 67.00 5 2.3 6 5 2.8 5 52.36 86.38 132.58 514.53

8 -0.356 0.725 1.809 0.564 -0.278 0.290 0.915 54.96 93.79 54.20 67.85 51.63 73.03 142.23 54.59 93.57 54.85 67.71 5 1.8 6 5 2.5 3 51.86 73.03 142.23 537.85

9 -1.392 0.669 1.082 -0.413 -1.821 1.191 0.366 47.45 93.33 50.44 63.09 43.99 79.74 131.50 47.94 93.08 50.44 62.94 4 3.5 2 4 9.5 6 43.52 79.74 131.50 509.16

10 -0.196 -0.671 0.513 1.099 -0.461 -1.749 -0.296 56.12 82.21 47.49 70.46 50.72 57.86 118.52 55.70 82.03 47.25 70.48 5 0.7 7 5 1.9 0 50.77 57.86 118.52 482.60

11 1.372 -0.693 -0.718 0.489 -1.270 -0.312 -0.953 67.48 82.04 41.11 67.49 46.71 68.55 105.67 67.81 81.87 41.00 67.34 4 6.0 6 5 0.0 7 46.06 68.55 105.67 478.30

12 -1.333 -2.119 -0.617 1.898 0.930 1.761 0.579 47.87 70.21 41.64 74.35 57.60 83.98 135.65 48.29 71.57 41.49 74.82 5 7.2 2 5 7.8 3 57.83 83.98 135.65 513.62

13 -0.233 -1.451 1.738 -0.090 -1.511 -0.508 0.186 55.85 75.74 53.83 64.66 45.52 67.10 127.96 55.44 76.21 54.40 64.48 4 4.8 5 4 9.7 9 44.85 67.10 127.96 490.45

14 -0.633 -1.166 0.070 0.583 -0.632 -0.216 0.699 52.95 78.11 45.20 67.94 49.87 69.27 138.01 52.73 78.30 44.90 67.81 4 9.7 4 5 1.3 9 49.74 69.27 138.01 500.75

15 0.664 -0.425 -1.346 0.051 -0.845 -1.453 0.459 62.35 84.26 37.87 65.35 48.82 60.06 133.30 62.05 83.96 38.15 65.17 4 8.4 7 5 0.8 5 48.47 60.06 133.30 491.15

16 1.053 -0.524 -0.319 0.117 0.152 -0.184 0.815 65.18 83.44 43.18 65.67 53.75 69.51 140.29 65.16 83.18 42.93 65.49 5 4.2 0 5 4.2 6 54.20 69.51 140.29 520.76

17 -0.672 -0.751 2.269 1.454 0.139 1.395 -1.015 52.66 81.55 56.58 72.19 53.69 81.26 104.45 52.47 81.42 57.83 72.38 5 4.1 4 5 4.2 0 54.14 81.26 104.45 503.95

18 1.095 1.574 -0.078 -1.336 -2.207 1.140 -0.400 65.48 100.84 44.43 58.59 42.08 79.36 116.49 65.50 101.38 44.14 58.75 4 2.2 2 4 9.4 0 42.22 79.36 116.49 507.83

19 0.098 -0.456 -0.445 -0.350 1.653 -0.131 0.232 58.25 84.00 42.53 63.39 61.18 69.90 128.86 57.80 83.71 42.32 63.24 5 8.5 0 6 0.7 4 60.74 69.90 128.86 506.57

20 1.619 0.700 1.283 0.961 -0.524 0.885 -0.602 69.28 93.58 51.48 69.78 50.41 77.46 112.53 69.95 93.35 51.63 69.75 5 0.3 9 5 1.7 0 50.39 77.46 112.53 525.07

21 -0.935 0.828 -1.435 -0.275 -1.163 0.306 0.214 50.76 94.64 37.41 63.76 47.25 73.15 128.51 50.77 94.48 37.76 63.60 4 6.6 4 5 0.2 3 46.64 73.15 128.51 494.91

22 1.300 1.771 3.141 1.175 0.514 -0.708 0.225 66.96 102.47 61.10 70.83 55.55 65.61 128.73 67.20 103.27 63.94 70.88 5 5.8 3 5 5.9 0 55.90 65.61 128.73 555.54

23 0.476 -0.167 -1.648 -1.364 -0.689 -0.115 0.691 60.99 86.39 36.30 58.45 49.59 70.02 137.85 60.61 86.02 36.84 58.62 4 9.4 0 5 1.2 3 49.40 70.02 137.85 499.36

24 2.328 2.545 -0.233 0.465 0.155 0.528 0.540 74.41 108.89 43.63 67.37 53.77 74.80 134.89 76.46 111.09 43.36 67.22 5 4.2 2 5 4.2 7 54.22 74.80 134.89 562.03

x4x5

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Page 15

25 1.189 -1.397 -0.459 -0.683 0.289 -0.192 0.587 66.16 76.20 42.46 61.77 54.43 69.45 135.82 66.28 76.61 42.25 61.69 5 4.8 6 5 4.8 6 54.86 69.45 135.82 506.95

26 -0.272 -0.282 1.187 1.102 0.420 0.120 -1.202 55.57 85.44 50.98 70.47 55.08 71.77 100.78 55.17 85.10 51.06 70.50 5 5.4 5 5 5.4 7 55.47 71.77 100.78 489.84

27 -2.454 0.461 -0.593 0.787 -0.619 1.053 -0.481 39.75 91.60 41.76 68.94 49.94 78.71 114.91 41.96 91.27 41.60 68.86 4 9.8 2 5 1.4 2 49.82 78.71 114.91 487.12

28 -0.572 1.413 0.004 -2.197 -0.537 -0.826 0.512 53.39 99.50 44.86 54.39 50.34 64.73 134.34 53.13 99.84 44.56 55.08 5 0.3 2 5 1.6 7 50.32 64.73 134.34 502.00

29 0.348 0.484 0.186 0.989 0.653 -0.652 0.744 60.06 91.80 45.80 69.92 56.23 66.03 138.89 59.64 91.47 45.50 69.90 5 6.3 6 5 6.5 5 56.55 66.03 138.89 527.98

30 0.846 -1.054 -0.768 0.295 -0.873 -0.603 1.352 63.67 79.04 40.86 66.54 48.68 66.39 150.79 63.48 79.12 40.77 66.36 4 8.3 0 5 0.7 8 48.30 66.39 150.79 515.22

31 -0.700 0.120 1.070 0.388 0.060 1.220 0.170 52.46 88.78 50.38 66.99 53.30 79.96 127.65 52.29 88.39 50.38 66.83 5 3.7 4 5 3.8 6 53.74 79.96 127.65 519.22

32 0.467 1.621 -0.956 -1.394 1.206 0.818 -0.497 60.93 101.23 39.88 58.31 58.97 76.96 114.58 60.53 101.82 39.90 58.49 5 7.8 6 5 9.0 4 59.04 76.96 114.58 511.33

33 0.525 -1.332 1.297 -2.509 -1.513 -0.669 0.614 61.35 76.73 51.55 52.87 45.51 65.89 136.34 60.98 77.07 51.71 53.81 4 4.8 4 4 9.7 9 44.84 65.89 136.34 490.65

34 0.697 1.398 0.985 -0.301 -0.243 -0.466 -0.442 62.59 99.38 49.93 63.63 51.80 67.41 115.66 62.31 99.71 49.89 63.47 5 2.0 6 5 2.6 5 52.06 67.41 115.66 510.50

35 -0.227 -1.073 -0.551 0.886 0.372 1.191 0.954 55.89 78.88 41.98 69.42 54.84 79.74 143.01 55.49 78.98 41.80 69.36 5 5.2 4 5 5.2 5 55.25 79.74 143.01 523.63

36 -0.368 0.761 -0.024 -1.543 -0.384 0.373 0.080 54.87 94.10 44.71 57.58 51.10 73.65 125.89 54.51 93.90 44.42 57.84 5 1.2 3 5 2.1 6 51.23 73.65 125.89 501.44

37 1.552 0.352 -0.673 -0.448 -0.273 -1.546 -1.443 68.79 90.70 41.35 62.91 51.65 59.37 96.06 69.37 90.34 41.22 62.78 5 1.8 8 5 2.5 4 51.88 59.37 96.06 471.02

38 0.488 0.449 -0.896 1.343 -1.010 0.618 -2.112 61.08 91.50 40.19 71.65 48.00 75.48 82.97 60.70 91.17 40.17 71.78 4 7.5 0 5 0.5 0 47.50 75.48 82.97 469.76

39 -1.394 -1.241 1.748 -0.255 -0.246 -0.132 0.612 47.43 77.49 53.88 63.86 51.78 69.89 136.31 47.92 77.74 54.46 63.69 5 2.0 4 5 2.6 4 52.04 69.89 136.31 502.06

40 -0.502 0.482 -0.249 0.864 0.645 -0.358 1.522 53.90 91.78 43.55 69.31 56.19 68.21 154.12 53.60 91.45 43.28 69.25 5 6.3 3 5 6.5 1 56.51 68.21 154.12 536.43

41 -1.827 -0.546 0.154 0.615 -0.017 -0.501 0.807 44.29 83.25 45.63 68.10 52.92 67.15 140.11 45.39 83.01 45.33 67.97 5 3.3 2 5 3.5 4 53.32 67.15 140.11 502.28

42 0.724 0.159 -1.919 0.112 1.183 0.894 0.962 62.79 89.10 34.90 65.65 58.85 77.53 143.16 62.52 88.71 35.71 65.47 5 7.8 1 5 8.9 4 58.94 77.53 143.16 532.03

43 1.119 -2.176 -0.550 -1.023 0.022 -0.691 -0.800 65.65 69.73 41.99 60.11 53.11 65.73 108.66 65.69 71.18 41.81 60.14 5 3.5 3 5 3.7 0 53.53 65.73 108.66 466.74

44 -0.007 0.402 -0.799 -0.239 0.021 -2.099 -0.507 57.49 91.11 40.70 63.94 53.10 55.26 114.39 57.04 90.77 40.63 63.77 5 3.5 3 5 3.7 0 53.53 55.26 114.39 475.37

45 -0.052 -0.608 -0.469 -0.670 0.891 0.955 -1.270 57.17 82.74 42.41 61.83 57.41 77.98 99.45 56.72 82.52 42.20 61.74 5 7.1 1 5 7.6 5 57.65 77.98 99.45 478.27

46 -0.316 -0.042 -0.198 0.853 -0.234 0.822 -0.597 55.25 87.43 43.81 69.26 51.84 76.99 112.63 54.87 87.05 43.54 69.19 5 2.1 1 5 2.6 9 52.11 76.99 112.63 496.38

47 -0.191 -0.036 2.413 0.670 -0.156 -0.299 0.905 56.16 87.48 57.33 68.37 52.23 68.65 142.04 55.74 87.10 58.80 68.25 5 2.5 6 5 2.9 8 52.56 68.65 142.04 533.14

48 -1.511 0.681 0.518 -1.589 -0.203 0.055 -0.951 46.59 93.43 47.52 57.36 51.99 71.29 105.70 47.23 93.19 47.28 57.65 5 2.2 9 5 2.8 0 52.29 71.29 105.70 474.61

49 -0.715 0.429 0.405 -0.121 1.226 -0.513 1.341 52.36 91.34 46.93 64.51 59.07 67.06 150.57 52.19 91.00 46.67 64.33 5 7.9 0 5 9.1 2 59.12 67.06 150.57 530.93

50 0.125 -0.666 -0.632 -0.175 1.541 -0.885 -1.084 58.44 82.26 41.56 64.25 60.63 64.29 103.09 57.99 82.07 41.42 64.07 5 8.3 8 6 0.3 5 60.35 64.29 103.09 473.28


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Page 16

APPENDIX 3: Simulation case r = -0.15

506.68

Min-Mid Mid-Max TPC

1 -1.116 -1.118 -1.149 -1.456 -1.158 -1.623 0.335 49.45 80.00 40.92 61.29 52.60 70.88 171.88 49.63 79.99 40.83 61.23 5 2.9 8 5 3.2 8 52.98 70.88 171.88 527.43

2 -0.146 0.721 0.739 -1.559 -0.035 -0.140 -0.656 56.48 93.88 48.02 56.62 53.56 71.17 120.10 56.05 93.66 47.81 57.00 5 4.0 1 5 4.0 9 54.01 71.17 120.10 499.80

3 -0.620 -1.437 -0.081 0.972 -0.079 -0.895 -0.469 53.05 76.76 46.21 71.36 53.18 66.24 129.66 52.82 77.10 45.92 71.47 5 3.6 1 5 3.7 6 53.61 66.24 129.66 496.82

4 -0.908 0.477 -1.407 -0.277 -0.316 1.632 -0.958 50.96 92.82 38.02 65.51 53.64 85.09 105.66 50.94 92.55 38.28 65.32 5 4.0 9 5 4.1 6 54.09 85.09 105.66 491.92

5 0.585 0.067 -0.512 -1.879 -1.141 -1.224 0.910 61.78 87.61 41.74 56.43 50.28 69.74 165.94 61.44 87.22 41.58 56.83 5 0.2 4 5 1.6 3 50.24 69.74 165.94 532.99

6 3.052 -0.011 -0.287 -0.727 0.350 -1.999 -0.601 79.67 83.89 41.03 59.80 53.56 55.82 129.83 83.73 83.61 40.93 59.85 5 4.0 1 5 4.0 9 54.01 55.82 129.83 507.78

7 1.190 -1.827 -0.659 0.413 0.794 0.824 0.353 66.17 71.31 42.24 68.37 57.44 75.31 118.81 66.29 72.47 42.04 68.25 5 7.1 3 5 7.6 8 57.68 75.31 118.81 500.86

8 0.376 -0.386 -1.389 0.049 -1.040 1.106 0.680 60.27 84.15 37.89 66.79 49.72 82.65 134.95 59.85 83.86 38.17 66.63 4 9.5 5 5 1.3 0 49.55 82.65 134.95 515.66

9 0.540 -0.691 -1.254 -0.730 -0.528 -0.546 0.811 61.46 81.44 38.72 63.19 53.04 72.42 153.68 61.09 81.31 38.88 63.04 5 3.4 6 5 3.6 4 53.46 72.42 153.68 523.88

10 -1.015 0.428 0.367 -2.190 -0.149 0.229 0.520 50.18 92.55 47.08 54.96 55.14 76.93 141.09 50.26 92.26 46.82 55.56 5 5.5 0 5 5.5 2 55.52 76.93 141.09 518.45

11 0.387 -1.684 -2.287 -0.784 -0.459 -0.385 0.489 60.35 73.48 34.53 64.94 55.46 76.43 155.66 59.93 74.28 35.42 64.76 5 5.7 6 5 5.8 2 55.82 76.43 155.66 522.31

12 -1.105 0.079 1.256 -2.056 -0.421 0.887 1.162 49.53 89.81 51.95 55.04 53.19 80.69 142.03 49.69 89.43 52.17 55.63 5 3.6 2 5 3.7 7 53.62 80.69 142.03 523.27

13 2.588 -0.839 1.395 0.569 -1.635 -1.154 -0.882 76.30 77.68 50.61 65.14 42.23 62.71 121.76 79.00 77.91 50.64 64.96 4 2.3 1 4 9.4 1 42.31 62.71 121.76 499.28

14 -0.192 -0.420 -1.396 -0.394 0.123 0.269 -1.553 56.15 84.58 38.33 65.19 56.01 75.95 109.89 55.73 84.26 38.54 65.01 5 6.1 9 5 6.3 4 56.34 75.95 109.89 485.72

15 -0.321 -1.666 -0.992 -0.159 1.017 0.016 -0.142 55.21 74.51 41.59 67.02 60.51 72.75 126.94 54.83 75.16 41.44 66.86 5 8.3 5 6 0.2 6 60.26 72.75 126.94 498.25

16 0.389 -2.025 -0.062 -0.732 -1.497 -0.847 1.627 60.36 70.69 46.05 63.21 48.68 73.06 174.16 59.94 71.96 45.76 63.06 4 8.3 1 5 0.7 9 48.31 73.06 174.16 536.25

17 0.336 0.160 -0.553 -0.192 -0.325 -1.612 0.649 59.98 88.68 41.64 64.39 51.96 62.18 152.88 59.55 88.28 41.49 64.21 5 2.2 5 5 2.7 7 52.25 62.18 152.88 520.84

18 0.187 -0.852 0.795 0.183 1.715 0.141 -1.044 58.90 80.56 49.47 65.73 60.30 66.70 95.73 58.44 80.51 49.37 65.55 5 8.3 0 6 0.1 1 60.11 66.70 95.73 476.40

19 2.539 -0.718 -0.403 -0.668 -0.323 0.735 -0.977 75.95 78.73 41.48 61.17 51.55 76.35 106.22 78.51 78.85 41.34 61.12 5 1.7 6 5 2.4 7 51.76 76.35 106.22 494.15

20 -1.286 0.444 -1.873 -1.370 -0.454 1.064 -1.152 48.22 93.02 36.00 61.22 55.21 85.16 118.34 48.58 92.75 36.59 61.16 5 5.5 5 5 5.5 8 55.58 85.16 118.34 498.17

21 -2.383 0.450 0.535 1.039 0.461 -0.271 -1.224 40.26 94.43 48.97 70.73 54.58 67.23 105.68 42.33 94.26 48.83 70.77 5 5.0 0 5 5.0 0 55.00 67.23 105.68 484.11

22 0.039 1.634 -0.977 -1.546 -0.083 0.543 -0.640 57.82 101.13 38.40 57.51 54.18 76.85 117.11 57.37 101.71 38.61 57.79 5 4.6 2 5 4.6 3 54.62 76.85 117.11 504.05

23 1.408 -0.780 -1.009 0.580 0.657 0.188 0.647 67.75 79.63 39.36 68.45 55.90 70.27 126.33 68.12 79.66 39.44 68.34 5 6.1 1 5 6.2 4 56.24 70.27 126.33 508.40

24 0.070 1.345 -0.967 -0.641 -1.962 -0.066 0.756 58.04 98.72 38.69 61.92 44.73 76.38 150.59 57.59 98.96 38.86 61.82 4 4.1 3 4 9.6 6 44.13 76.38 150.59 528.33

x4x5

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Page 17

25 0.313 -0.401 0.624 0.057 0.662 0.430 0.535 59.81 84.10 48.10 64.84 55.39 70.99 120.31 59.38 83.81 47.89 64.66 5 5.7 1 5 5.7 6 55.76 70.99 120.31 502.80

26 1.127 0.853 0.121 0.527 -0.780 -1.406 -0.180 65.71 93.37 43.80 65.87 47.09 60.43 131.77 65.76 93.13 43.52 65.69 4 6.4 7 5 0.1 8 46.47 60.43 131.77 506.77

27 -0.173 0.180 -1.391 -0.239 -0.611 -0.759 0.177 56.29 89.47 37.80 65.38 51.95 70.23 145.12 55.87 89.08 38.09 65.20 5 2.2 4 5 2.7 7 52.24 70.23 145.12 515.82

28 -1.428 1.309 -1.318 1.658 1.758 -1.457 -0.141 47.18 100.29 38.12 74.05 60.12 55.94 121.84 47.72 100.75 38.36 74.48 5 8.2 5 5 9.9 7 59.97 55.94 121.84 499.06

29 1.415 0.390 -0.467 0.878 1.671 -0.099 -0.060 67.80 89.21 41.03 68.27 58.53 62.93 105.25 68.18 88.83 40.93 68.16 5 7.6 8 5 8.6 6 58.66 62.93 105.25 492.94

30 0.773 -0.073 0.091 -0.683 -0.106 -0.336 0.016 63.14 86.22 44.76 61.34 52.79 69.43 129.67 62.90 85.85 44.47 61.28 5 3.1 9 5 3.4 4 53.19 69.43 129.67 506.79

31 -1.635 1.395 -1.898 -0.345 -0.083 -2.013 0.872 45.69 101.26 35.28 65.44 55.04 62.01 166.04 46.50 101.86 36.01 65.26 5 5.4 1 5 5.4 2 55.42 62.01 166.04 533.11

32 -0.983 0.791 0.207 -0.706 0.353 -0.342 0.300 50.41 95.49 45.93 61.67 55.34 68.93 132.26 50.46 95.40 45.63 61.59 5 5.6 6 5 5.7 1 55.71 68.93 132.26 509.97

33 -0.872 0.388 -0.275 -0.349 0.286 0.489 -0.196 51.22 92.05 43.77 64.07 55.34 74.80 119.06 51.17 91.73 43.50 63.90 5 5.6 7 5 5.7 1 55.71 74.80 119.06 499.87

34 1.354 0.218 0.796 0.505 -2.060 -0.496 -1.319 67.36 87.88 47.60 65.45 41.01 69.00 115.05 67.67 87.49 47.36 65.27 4 1.6 7 4 9.3 6 41.67 69.00 115.05 493.50

35 -2.408 -0.712 -0.417 0.409 0.823 -2.737 0.483 40.08 84.94 45.25 69.78 59.03 54.98 161.60 42.20 84.61 44.95 69.76 5 7.8 9 5 9.1 0 59.10 54.98 161.60 517.19

36 0.296 0.197 -0.436 -1.648 -0.012 0.058 -0.921 59.68 89.03 42.23 57.52 55.12 74.55 120.20 59.25 88.64 42.03 57.79 5 5.4 8 5 5.5 0 55.50 74.55 120.20 497.96

37 -1.083 0.194 0.365 0.335 -0.208 0.370 0.300 49.69 90.72 47.34 66.91 51.89 73.48 125.34 49.84 90.36 47.09 66.74 5 2.1 7 5 2.7 2 52.17 73.48 125.34 505.02

38 0.359 0.518 -0.226 2.202 -1.736 -0.845 -1.810 60.14 91.58 42.95 74.83 41.84 65.00 107.27 59.72 91.25 42.71 75.37 4 2.0 8 4 9.3 9 42.08 65.00 107.27 483.41

39 -0.994 -0.370 1.165 0.817 -0.244 0.604 -2.821 50.33 85.98 51.81 68.74 50.70 73.52 77.75 50.39 85.62 52.01 68.65 5 0.7 5 5 1.8 9 50.75 73.52 77.75 458.70

40 2.469 -0.940 0.205 0.631 1.655 -1.322 -0.671 75.44 77.00 44.80 66.81 58.45 55.24 109.38 77.83 77.31 44.50 66.64 5 7.6 4 5 8.5 9 58.59 55.24 109.38 489.50

41 -1.110 -1.148 -1.725 -0.755 1.156 -1.802 1.497 49.50 79.74 38.04 65.15 62.80 63.42 172.43 49.67 79.76 38.30 64.96 5 8.7 5 6 1.7 3 61.73 63.42 172.43 530.27

42 0.200 -1.707 0.481 -0.531 -1.113 0.852 1.023 58.99 73.53 48.64 63.46 49.48 81.36 142.87 58.54 74.32 48.47 63.30 4 9.2 6 5 1.1 7 49.26 81.36 142.87 518.13

43 0.560 0.209 0.354 -0.447 0.571 -0.521 0.471 61.60 88.80 46.00 62.08 55.19 65.55 130.39 61.25 88.41 45.70 61.98 5 5.5 4 5 5.5 7 55.57 65.55 130.39 508.85

44 0.037 0.702 -1.356 0.989 -0.866 -0.096 0.609 57.81 93.49 37.34 70.44 48.58 71.72 137.19 57.36 93.25 37.70 70.46 4 8.1 8 5 0.7 4 48.18 71.72 137.19 515.86

45 1.833 -0.254 -0.560 -0.918 -1.079 0.919 -0.699 70.83 83.41 40.82 60.29 48.73 80.35 115.56 71.85 83.16 40.74 60.30 4 8.3 6 5 0.8 1 48.36 80.35 115.56 500.32

46 0.830 -0.707 -0.084 0.662 -0.057 -0.734 -0.376 63.56 80.94 44.41 68.25 51.97 65.24 123.98 63.36 80.86 44.12 68.13 5 2.2 6 5 2.7 9 52.26 65.24 123.98 497.95

47 -0.626 0.372 0.115 0.455 -0.603 -0.284 0.212 53.00 91.61 45.57 67.23 49.71 69.78 131.81 52.78 91.27 45.27 67.08 4 9.5 5 5 1.3 0 49.55 69.78 131.81 507.53

48 -0.074 -0.127 -1.192 0.068 -0.474 0.237 0.591 57.00 86.83 39.00 66.79 52.16 75.55 138.16 56.56 86.45 39.12 66.62 5 2.4 8 5 2.9 3 52.48 75.55 138.16 514.94

49 -1.694 2.095 2.893 -0.934 0.146 0.886 -0.826 45.26 107.07 58.84 57.29 51.32 72.58 94.30 46.15 108.82 60.80 57.59 5 1.5 0 5 2.3 1 51.50 72.58 94.30 491.73

50 0.116 1.586 -1.053 -0.592 0.537 -0.123 2.481 58.38 100.65 38.01 61.99 55.82 69.32 156.42 57.93 101.15 38.27 61.89 5 6.0 5 5 6.1 6 56.16 69.32 156.42 541.15


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Page 18

assigment 2 - total project cost

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