Decision Modelling with Spreadsheets: Solver Solutions and Analysis

This document presents solutions to several decision modelling problems using spreadsheets and Excel Solver. The first problem focuses on project selection to maximize Net Present Value (NPV) for TMC Corporation, considering integer constraints and engineer allocation. The solution utilizes the GRG non-linear algorithm, providing an answer report and highlighting binding and non-binding constraints. The second problem explores optimal flow between nodes in New York City, maximizing the probability of no failure, with analysis of sensitivity reports and Lagrange multipliers. The third problem addresses portfolio optimization, minimizing the sum of variance of different scenarios, with detailed solver results and sensitivity analysis. The final two problems focus on optimizing football team ratings, first maximizing average correct estimated victories and then maximizing the sum of squares of correct estimates, with detailed reports and analysis of the solver results and sensitivity reports.

Running head: DECISION MODELLING WITH SPREADSHEETS
DECISION MODELLING WITH SPREADSHEETS
Name of Student:
Name of University:
Author Note:

1DECISION MODELLING WITH SPREADSHEETS
Table of Contents
Answer to 8-6:............................................................................................................................2
Answer to 8-6:............................................................................................................................3
Answer to 8-34:..........................................................................................................................5
Answer to question 8-42-2:........................................................................................................6
Answer to question 8-42-1:........................................................................................................9
Reference List..........................................................................................................................12

2DECISION MODELLING WITH SPREADSHEETS
Answer to 8-6:
In the problem the optimal selection of projects from 1 to 6 and the optimum
engineers included in those project is found that gives the maximum expected Net Present
Value of TMC Corporation satisfying all the constraints as specified in spreadsheet. The
selected status of the project is represented by 1 and not selected status is represented by 0.
Now, as found using solver the project 1, 3,4 and 5 when selected with engineers 4,6,6 and 9
then the project delivers maximum expected NPV of $1719.30. As there are integer
constraints in the model (Select = binary integers 0 or 1) hence sensitivity analysis is not
valid and thus only answer report is generated.
From the answer report it is clear that the GRG non-linear algorithm finds the optimal
solution of the problem under specified limit of iteration time of 100 sec, 1000 iterations and
solution is under limit of 10^(-7) precision satisfying all constraints. Also, the answer report
shows that nine constraints in the optimal solution are not binding i.e. not reaches to
maximum limit specified (thus there is slack) and rest are bounded as shown below.

3DECISION MODELLING WITH SPREADSHEETS
Constraints
Cell Name Cell Value Formula Status Slack
$C$13 Total Used Assigned 25 $C$13<=$C$14 Binding 0
$D$7 Constraints -21 $D$7<=0 Not Binding 21
$D$8 Constraints 0 $D$8<=0 Binding 0
$D$9 Constraints -19 $D$9<=0 Not Binding 19
$D$10 Constraints -19 $D$10<=0 Not Binding 19
$D$11 Constraints -16 $D$11<=0 Not Binding 16
$D$12 Constraints 0 $D$12<=0 Binding 0
$F$7 Success 0.5634 $F$7>=$G$7 Not Binding 0.0634
$F$8 Success 0.0000 $F$8>=$G$8 Binding 0.0000
$F$9 Success 0.5714 $F$9>=$G$9 Not Binding 0.0714
$F$10 Success 0.5172 $F$10>=$G$10 Not Binding 0.0172
$F$11 Success 0.5233 $F$11>=$G$11 Not Binding 0.0233
$F$12 Success 0.0000 $F$12>=$G$12 Binding 0.0000
$J$13 Total Cost 1,650.00₹ $J$13<=$J$14 Not Binding 50
$C$7 Assigned 4 $C$7>=0 Binding 0
$C$8 Assigned 0 $C$8>=0 Binding 0
$C$9 Assigned 6 $C$9>=0 Binding 0
$C$10 Assigned 6 $C$10>=0 Binding 0
$C$11 Assigned 9 $C$11>=0 Binding 0
$C$12 Assigned 0 $C$12>=0 Binding 0
$B$7:$B$12=Binary
$C$7:$C$12=Integer
Select? Engineers Linking Probability Prob. of L.B. Prob. of NPV if Expected Startup
Project (1=y, 0=n) Assigned Constraints Parameter Success Success Successful NPV Cost
1 1 4 -21 3.1 0.5634 0.5000 $750.00 $422.54 $325.00
2 0 0 0 2.5 0.0000 0.0000 $120.00 $0.00 $200.00
3 1 6 -19 4.5 0.5714 0.5000 $900.00 $514.29 $490.00
4 1 6 -19 5.6 0.5172 0.5000 $400.00 $206.90 $125.00
5 1 9 -16 8.2 0.5233 0.5000 $1,100.00 $575.58 $710.00
6 0 0 0 8.5 0.0000 0.0000 $800.00 $0.00 $240.00
Total Used 25 Total $1,719.30 $1,650.00
Total Available 25 Startup Funds Available $1,700.00
Answer to 8-6:
In this problem the optimal flow between the nodes of New York City are calculated
using solver GRG non-linear engine such that the probability of no failure is maximized. The
answer report shows that all the constraints of the variable are not bounded to it maximum
value as below (Hair et al., 2017). The sensitivity report shows that the gradient for all the
variables are either 0 or very close to zero signifying a local maximum is found as the change

4DECISION MODELLING WITH SPREADSHEETS
in variables does not affect the objective function value by much. The Lagrange’s multiplier
values show if the constraints are increased by one then how much it will change the
objective function. As Lagrange’s multiplier values are very close to zero hence an unit or
small change will not affect the value of probability of no failure.
From To Lower Upper Prob of Prob of
Flow Node Node Bound Bound Parameter Failure No Failure Node Net Flow
80 1 2 0 80 0.10 0.008 0.992 1 0
30 1 3 0 50 0.17 0.005 0.995 2 0
20 2 4 0 90 0.19 0.004 0.996 3 0
60 2 5 0 60 0.15 0.009 0.991 4 0
30 3 4 0 50 0.14 0.004 0.996 5 0
0 3 5 0 70 0.16 0.000 1.000 6 0
50 4 6 0 70 0.11 0.005 0.995
60 5 6 0 60 0.09 0.005 0.995
110 6 1 110 999 0 0.000 1.000
0.960
Variable Cells
Final Reduced
Cell Name Value Gradient
$A$6 Flow 80 1.91966E-05
$A$7 Flow 30 0
$A$8 Flow 19.999999 0
$A$9 Flow 60.000001 5.75898E-05
$A$10 Flow 30 0
$A$11 Flow 0 -1.60071E-10
$A$12 Flow 49.999999 0
$A$13 Flow 60.000001 0
$A$14 Flow 110 -0.000403128
Constraints
Final Lagrange
Cell Name Value Multiplier
$K$6 Net Flow 0 0
$K$7 Net Flow 0 -0.00011518
$K$8 Net Flow 0 -0.000163171
$K$9 Net Flow 0 -0.000297547
$K$10 Net Flow 0 -0.000316744
$K$11 Net Flow 0 -0.000403128

5DECISION MODELLING WITH SPREADSHEETS
Constraints
Cell Name Cell Value Formula Status Slack
$K$6 Net Flow 0 $K$6=0 Binding 0
$K$7 Net Flow 0 $K$7=0 Binding 0
$K$8 Net Flow 0 $K$8=0 Binding 0
$K$9 Net Flow 0 $K$9=0 Binding 0
$K$10 Net Flow 0 $K$10=0 Binding 0
$K$11 Net Flow 0 $K$11=0 Binding 0
$A$14 Flow 110 $A$14>=$A$16 Binding 0
$A$6 Flow 80 $A$6<=$E$6 Binding 0
$A$7 Flow 30 $A$7<=$E$7 Not Binding 20
$A$8 Flow 19.999999 $A$8<=$E$8 Not Binding 70.000001
$A$9 Flow 60.000001 $A$9<=$E$9 Binding 0
$A$10 Flow 30 $A$10<=$E$10 Not Binding 20
$A$11 Flow 0 $A$11<=$E$11 Not Binding 70
$A$12 Flow 49.999999 $A$12<=$E$12 Not Binding 20.000001
$A$13 Flow 60.000001 $A$13<=$E$13 Binding 0
$A$14 Flow 110 $A$14<=$E$14 Not Binding 889
$A$6 Flow 80 $A$6>=$D$6 Not Binding 80
$A$7 Flow 30 $A$7>=$D$7 Not Binding 30
$A$8 Flow 19.999999 $A$8>=$D$8 Not Binding 19.999999
$A$9 Flow 60.000001 $A$9>=$D$9 Not Binding 60.000001
$A$10 Flow 30 $A$10>=$D$10 Not Binding 30
$A$11 Flow 0 $A$11>=$D$11 Binding 0
$A$12 Flow 49.999999 $A$12>=$D$12 Not Binding 49.999999
$A$13 Flow 60.000001 $A$13>=$D$13 Not Binding 60.000001
$A$14 Flow 110 $A$14>=$D$14 Binding 0
$A$6 Flow 80 $A$6>=0 Not Binding 80
$A$7 Flow 30 $A$7>=0 Not Binding 30
$A$8 Flow 19.999999 $A$8>=0 Not Binding 19.999999
$A$9 Flow 60.000001 $A$9>=0 Not Binding 60.000001
$A$10 Flow 30 $A$10>=0 Not Binding 30
$A$11 Flow 0 $A$11>=0 Binding 0
$A$12 Flow 49.999999 $A$12>=0 Not Binding 49.999999
$A$13 Flow 60.000001 $A$13>=0 Not Binding 60.000001
$A$14 Flow 110 $A$14>=0 Binding 0
Answer to 8-34:
In the portfolio optimization problem the optimal weights of different portfolios are
needed to be found such that the sum of variance of different scenarios are minimized. The
minimum value of sum of variance is found by excel solver as 0.002 for weights 0.207,
0.336, 0.106 and 0.351 respectively (Tripathi & Srivastava, 2017). The answer report shows
the constraints of four portfolio weights are not binding where return weights and sum of
Weights Windsor is bounded. From the sensitivity report the reduced gradient for all the
decision variables are found to be zero and hence the local optimum is found perfectly. Also,

6DECISION MODELLING WITH SPREADSHEETS
the Lagrange’s multiplier value for two constraints are found to be very close to zero or
changing the constraint values by an unit affects the sum of variance of different scenarios
very less amount.
Expected
Scenario Windsor Flagship Templeman T-Bills Return Probability Return Variance
1 0.14 -0.09 0.1 0.07 0.034 0.1 0.34% 0.001
2 -0.11 0.12 0.14 0.06 0.053 0.1 0.53% 0.000
3 0.09 0.15 -0.11 0.08 0.086 0.1 0.86% 0.000
4 0.25 0.18 0.33 0.07 0.172 0.3 5.15% 0.001
5 0.18 0.16 0.15 0.06 0.128 0.4 5.12% 0.000
Weights 0.207 0.336 0.106 0.351 12.00% 0.002
Sum of Weights 1 12.00%
Variable Cells
Final Reduced
Cell Name Value Gradient
$B$12 Weights Windsor 0.207276288 0
$C$12 Weights Flagship 0.336269475 0
$D$12 Weights Templeman 0.1055136 0
$E$12 Weights T-Bills 0.350940636 0
Constraints
Final Lagrange
Cell Name Value Multiplier
$B$13 Sum of Weights Windsor 1 -0.005212337
$H$12 Weights Return 0.12 0.078980813
Constraints
Cell Name Cell Value Formula Status Slack
$B$13 Sum of Weights Windsor 1 $B$13=1 Binding 0
$H$12 Weights Return 12.00% $H$12>=$H$13 Binding 0.00%
$B$12 Weights Windsor 0.207 $B$12>=0 Not Binding 0.207
$C$12 Weights Flagship 0.336 $C$12>=0 Not Binding 0.336
$D$12 Weights Templeman 0.106 $D$12>=0 Not Binding 0.106
$E$12 Weights T-Bills 0.351 $E$12>=0 Not Binding 0.351
Answer to question 8-42-2:
In this problem the optimum rating of football teams are needed to be found with
rating of home field advantage such that average number correct estimated victories can be
maximized. It can be seen from the results that the maximum value of average correct
estimated victories is 0.9055 as found using excel solver with GRG non-linear engine
satisfying all constraints. The answer report shows that none of the variables are binding to its

7DECISION MODELLING WITH SPREADSHEETS
maximum limit in the optimal solution. The reduced gradient is exactly zero from the
sensitivity zero signifying that the optimal solution is reached perfectly within limited
number of iterations and well below the precision limit.
Team Name Rating
Visiting
Team
Home
Team
Margin of Home Team
Victory (or Loss) Est. Margin Correct?
Atlanta Eagles 28.764 16 1 -2 15.7916 0 Total correct 0.9055
Buffalo Wings 38.1814 13 1 3 5.78419047 1
Chicago Grizzlies 31.2523 18 1 -22 -6.98521028 1
Cincinnati Tigers 15.2856 14 1 16 17.4138009 1
Cleveland Reds 25.7786 25 1 2 11.876745 1
Dallas Cowpokes 38.5685 15 2 3 21.5730717 1
Denver Bravos 30.8285 23 2 17 26.2420384 1
Detroit Leopards 22.4788 3 2 14 12.7055343 1
Green Bay Pickers 22.5128 11 2 35 34.0647689 1
Houston Greasers 40.4326 4 2 11 28.6722061 1
Indianapolis Ponies 9.89309 17 2 4 27.6069322 1
Kansas City Indians 31.814 16 3 3 18.2799186 1
Los Angeles Pirates 28.7563 19 3 2 12.4767444 1
Los Angeles Goats 17.1267 20 3 5 4.97599009 1
Miami Tarpons 22.3848 28 3 -14 -14.9726163 1
Minnesota Raiders 18.7489 9 3 9 14.516008 1
New England Volunteers 16.3509 8 3 9 14.5500412 1
New Orleans Sinners 41.5257 10 4 -24 -19.370402 1
New York Midgets 24.5521 28 4 -8 -30.9392881 1
New York Rockets 32.0528 26 4 -7 -8.3283984 1
Philadelphia Hawks 13.7743 6 5 -13 -7.0133977 1
Phoenix Sparrows 23.5421 4 5 1 16.2694613 1
Pittsburgh Robbers 17.7158 20 5 -4 -0.49772255 1
San Diego Checkers 12.1264 23 5 2 13.8392937 1
San Francisco 39ers 22.6638 28 6 -3 -7.65642909 1
Seattle Sea Lions 29.3905 21 6 -25 30.5706627 0
Tampa Bay Raiders 8.31141 19 6 4 19.7929316 1
Washington Pigskins 52.0014 4 6 11 29.0593612 1
22 6 19 20.8029217 1
Home Field Advantage 5.7765 4 7 30 21.3193667 1
Maximize: K5
By changing: C5:C32,C34
Subject to: 0<=C5:C32<=100
0<=C34<=20

8DECISION MODELLING WITH SPREADSHEETS
Constraints
Cell Name Cell Value Formula Status Slack
$C$34 Home Field Advantage Rating 3.038016604 $C$34<=20 Not Binding 16.9619834
$C$34 Home Field Advantage Rating 3.038016604 $C$34>=0 Not Binding 3.0380166
$C$5 Atlanta Eagles Rating 15.86861954 $C$5<=100 Not Binding 84.13138046
$C$6 Buffalo Wings Rating 14.57659441 $C$6<=100 Not Binding 85.42340559
$C$7 Chicago Grizzlies Rating 15.1552189 $C$7<=100 Not Binding 84.8447811
$C$8 Cincinnati Tigers Rating 8.381084777 $C$8<=100 Not Binding 91.61891522
$C$9 Cleveland Reds Rating 14.09584638 $C$9<=100 Not Binding 85.90415362
$C$10 Dallas Cowpokes Rating 19.71114816 $C$10<=100 Not Binding 80.28885184
$C$11 Denver Bravos Rating 18.38781576 $C$11<=100 Not Binding 81.61218424
$C$12 Detroit Leopards Rating 7.69126645 $C$12<=100 Not Binding 92.30873355
$C$13 Green Bay Pickers Rating 11.61570711 $C$13<=100 Not Binding 88.38429289
$C$14 Houston Greasers Rating 29.05003489 $C$14<=100 Not Binding 70.94996511
$C$15 Indianapolis Ponies Rating 0.000220704 $C$15<=100 Not Binding 99.9997793
$C$16 Kansas City Indians Rating 21.56181459 $C$16<=100 Not Binding 78.43818541
$C$17 Los Angeles Pirates Rating 14.68984673 $C$17<=100 Not Binding 85.31015327
$C$18 Los Angeles Goats Rating 12.00686273 $C$18<=100 Not Binding 87.99313727
$C$19 Miami Tarpons Rating 9.082696057 $C$19<=100 Not Binding 90.91730394
$C$20 Minnesota Raiders Rating 17.23393955 $C$20<=100 Not Binding 82.76606045
$C$21 New England Volunteers Rating 7.68790325 $C$21<=100 Not Binding 92.31209675
$C$22 New Orleans Sinners Rating 24.27498564 $C$22<=100 Not Binding 75.72501436
$C$23 New York Midgets Rating 13.36636316 $C$23<=100 Not Binding 86.63363684
$C$24 New York Rockets Rating 14.44663847 $C$24<=100 Not Binding 85.55336153
$C$25 Philadelphia Hawks Rating 16.96401559 $C$25<=100 Not Binding 83.03598441
$C$26 Phoenix Sparrows Rating 9.765315699 $C$26<=100 Not Binding 90.2346843
$C$27 Pittsburgh Robbers Rating 11.03704727 $C$27<=100 Not Binding 88.96295273
$C$28 San Diego Checkers Rating 12.0133421 $C$28<=100 Not Binding 87.9866579
$C$29 San Francisco 39ers Rating 21.15470731 $C$29<=100 Not Binding 78.84529269
$C$30 Seattle Sea Lions Rating 20.20338866 $C$30<=100 Not Binding 79.79661134
$C$31 Tampa Bay Raiders Rating 4.512444896 $C$31<=100 Not Binding 95.4875551
$C$32 Washington Pigskins Rating 31.79353899 $C$32<=100 Not Binding 68.20646101
$C$5 Atlanta Eagles Rating 15.86861954 $C$5>=0 Not Binding 15.8686195
$C$6 Buffalo Wings Rating 14.57659441 $C$6>=0 Not Binding 14.5765944
$C$7 Chicago Grizzlies Rating 15.1552189 $C$7>=0 Not Binding 15.1552189
$C$8 Cincinnati Tigers Rating 8.381084777 $C$8>=0 Not Binding 8.38108478
$C$9 Cleveland Reds Rating 14.09584638 $C$9>=0 Not Binding 14.0958464
$C$10 Dallas Cowpokes Rating 19.71114816 $C$10>=0 Not Binding 19.7111482
$C$11 Denver Bravos Rating 18.38781576 $C$11>=0 Not Binding 18.3878158
$C$12 Detroit Leopards Rating 7.69126645 $C$12>=0 Not Binding 7.69126645
$C$13 Green Bay Pickers Rating 11.61570711 $C$13>=0 Not Binding 11.6157071
$C$14 Houston Greasers Rating 29.05003489 $C$14>=0 Not Binding 29.0500349
$C$15 Indianapolis Ponies Rating 0.000220704 $C$15>=0 Not Binding 0.0002207
$C$16 Kansas City Indians Rating 21.56181459 $C$16>=0 Not Binding 21.5618146
$C$17 Los Angeles Pirates Rating 14.68984673 $C$17>=0 Not Binding 14.6898467
$C$18 Los Angeles Goats Rating 12.00686273 $C$18>=0 Not Binding 12.0068627
$C$19 Miami Tarpons Rating 9.082696057 $C$19>=0 Not Binding 9.08269606
$C$20 Minnesota Raiders Rating 17.23393955 $C$20>=0 Not Binding 17.2339396
$C$21 New England Volunteers Rating 7.68790325 $C$21>=0 Not Binding 7.68790325
$C$22 New Orleans Sinners Rating 24.27498564 $C$22>=0 Not Binding 24.2749856
$C$23 New York Midgets Rating 13.36636316 $C$23>=0 Not Binding 13.3663632
$C$24 New York Rockets Rating 14.44663847 $C$24>=0 Not Binding 14.4466385
$C$25 Philadelphia Hawks Rating 16.96401559 $C$25>=0 Not Binding 16.9640156
$C$26 Phoenix Sparrows Rating 9.765315699 $C$26>=0 Not Binding 9.7653157
$C$27 Pittsburgh Robbers Rating 11.03704727 $C$27>=0 Not Binding 11.0370473
$C$28 San Diego Checkers Rating 12.0133421 $C$28>=0 Not Binding 12.0133421
$C$29 San Francisco 39ers Rating 21.15470731 $C$29>=0 Not Binding 21.1547073
$C$30 Seattle Sea Lions Rating 20.20338866 $C$30>=0 Not Binding 20.2033887
$C$31 Tampa Bay Raiders Rating 4.512444896 $C$31>=0 Not Binding 4.5124449
$C$32 Washington Pigskins Rating 31.79353899 $C$32>=0 Not Binding 31.793539

9DECISION MODELLING WITH SPREADSHEETS
Answer to question 8-42-1:
Now, in this problem instead of maximizing the average correct estimates, the sum of
square of the correct estimates are maximized by changing ratings of football teams and the
home field advantage (Tripathi & Srivastava, 2017). The results as obtained from the solver
GRG non-linear engine show the maximum value of SSE is 14227 with optimum rating as
given below. The answer report shows that the decision variable i.e. the ratings of football
teams are not binding to their maximum values in the optimum solution. Also, the sensitivity
report shows that the reduced gradients of the decision variable are exactly equal to zero
signifying that a local maximum is found appropriately within precision limit and specified
number of iterations.
Team No. Team Name Rating
Visiting
Team
Home
Team
Margin of Home Team
Victory (or Loss) Est. Margin Correct?
1 Atlanta Eagles 15.8686 16 1 -2 1.67269659 0 SSE 14227
2 Buffalo Wings 14.5766 13 1 3 4.21678942 1
3 Chicago Grizzlies 15.1552 18 1 -22 -5.36834949 1
4 Cincinnati Tigers 8.38108 14 1 16 6.89977341 1
5 Cleveland Reds 14.0958 25 1 2 -2.24807116 0
6 Dallas Cowpokes 19.7111 15 2 3 8.53191496 1
7 Denver Bravos 18.3878 23 2 17 6.57756374 1
8 Detroit Leopards 7.69127 3 2 14 2.45939212 1
9 Green Bay Pickers 11.6157 11 2 35 17.6143903 1
10 Houston Greasers 29.05 4 2 11 9.23352624 1
11 Indianapolis Ponies 0.00022 17 2 4 9.92670776 1
12 Kansas City Indians 21.5618 16 3 3 0.95929595 1
13 Los Angeles Pirates 14.6898 19 3 2 4.82687234 1
14 Los Angeles Goats 12.0069 20 3 5 3.74659703 1
15 Miami Tarpons 9.0827 28 3 -14 -13.6003035 1
16 Minnesota Raiders 17.2339 9 3 9 6.57752839 1
17 New England Volunteers 7.6879 8 3 9 10.5019691 1
18 New Orleans Sinners 24.275 10 4 -24 -17.6309335 1
19 New York Midgets 13.3664 28 4 -8 -20.3744376 1
20 New York Rockets 14.4466 26 4 -7 -8.78428728 1
21 Philadelphia Hawks 16.964 6 5 -13 -2.57728518 1
22 Phoenix Sparrows 9.76532 4 5 1 8.75277821 1
23 Pittsburgh Robbers 11.037 20 5 -4 2.68722451 0
24 San Diego Checkers 12.0133 23 5 2 6.09681571 1
25 San Francisco 39ers 21.1547 28 6 -3 -9.04437423 1
26 Seattle Sea Lions 20.2034 21 6 -25 5.78514917 0
27 Tampa Bay Raiders 4.51244 19 6 4 9.38280161 1
28 Washington Pigskins 31.7935 4 6 11 14.36808 1
22 6 19 12.9838491 1
Home Field Advantage 3.03802 4 7 30 13.0447476 1
Minimize: K5
By changing: C5:C32,C34
Subject to: 0<=C5:C32<=100
0<=C34<=20

10DECISION MODELLING WITH SPREADSHEETS
Constraints
Cell Name Cell Value Formula Status Slack
$C$34 Home Field Advantage Rating 3.038016604 $C$34<=20 Not Binding 16.9619834
$C$34 Home Field Advantage Rating 3.038016604 $C$34>=0 Not Binding 3.0380166
$C$5 Atlanta Eagles Rating 15.86861954 $C$5<=100 Not Binding 84.13138046
$C$6 Buffalo Wings Rating 14.57659441 $C$6<=100 Not Binding 85.42340559
$C$7 Chicago Grizzlies Rating 15.1552189 $C$7<=100 Not Binding 84.8447811
$C$8 Cincinnati Tigers Rating 8.381084777 $C$8<=100 Not Binding 91.61891522
$C$9 Cleveland Reds Rating 14.09584638 $C$9<=100 Not Binding 85.90415362
$C$10 Dallas Cowpokes Rating 19.71114816 $C$10<=100 Not Binding 80.28885184
$C$11 Denver Bravos Rating 18.38781576 $C$11<=100 Not Binding 81.61218424
$C$12 Detroit Leopards Rating 7.69126645 $C$12<=100 Not Binding 92.30873355
$C$13 Green Bay Pickers Rating 11.61570711 $C$13<=100 Not Binding 88.38429289
$C$14 Houston Greasers Rating 29.05003489 $C$14<=100 Not Binding 70.94996511
$C$15 Indianapolis Ponies Rating 0.000220704 $C$15<=100 Not Binding 99.9997793
$C$16 Kansas City Indians Rating 21.56181459 $C$16<=100 Not Binding 78.43818541
$C$17 Los Angeles Pirates Rating 14.68984673 $C$17<=100 Not Binding 85.31015327
$C$18 Los Angeles Goats Rating 12.00686273 $C$18<=100 Not Binding 87.99313727
$C$19 Miami Tarpons Rating 9.082696057 $C$19<=100 Not Binding 90.91730394
$C$20 Minnesota Raiders Rating 17.23393955 $C$20<=100 Not Binding 82.76606045
$C$21 New England Volunteers Rating 7.68790325 $C$21<=100 Not Binding 92.31209675
$C$22 New Orleans Sinners Rating 24.27498564 $C$22<=100 Not Binding 75.72501436
$C$23 New York Midgets Rating 13.36636316 $C$23<=100 Not Binding 86.63363684
$C$24 New York Rockets Rating 14.44663847 $C$24<=100 Not Binding 85.55336153
$C$25 Philadelphia Hawks Rating 16.96401559 $C$25<=100 Not Binding 83.03598441
$C$26 Phoenix Sparrows Rating 9.765315699 $C$26<=100 Not Binding 90.2346843
$C$27 Pittsburgh Robbers Rating 11.03704727 $C$27<=100 Not Binding 88.96295273
$C$28 San Diego Checkers Rating 12.0133421 $C$28<=100 Not Binding 87.9866579
$C$29 San Francisco 39ers Rating 21.15470731 $C$29<=100 Not Binding 78.84529269
$C$30 Seattle Sea Lions Rating 20.20338866 $C$30<=100 Not Binding 79.79661134
$C$31 Tampa Bay Raiders Rating 4.512444896 $C$31<=100 Not Binding 95.4875551
$C$32 Washington Pigskins Rating 31.79353899 $C$32<=100 Not Binding 68.20646101
$C$5 Atlanta Eagles Rating 15.86861954 $C$5>=0 Not Binding 15.8686195
$C$6 Buffalo Wings Rating 14.57659441 $C$6>=0 Not Binding 14.5765944
$C$7 Chicago Grizzlies Rating 15.1552189 $C$7>=0 Not Binding 15.1552189
$C$8 Cincinnati Tigers Rating 8.381084777 $C$8>=0 Not Binding 8.38108478
$C$9 Cleveland Reds Rating 14.09584638 $C$9>=0 Not Binding 14.0958464
$C$10 Dallas Cowpokes Rating 19.71114816 $C$10>=0 Not Binding 19.7111482
$C$11 Denver Bravos Rating 18.38781576 $C$11>=0 Not Binding 18.3878158
$C$12 Detroit Leopards Rating 7.69126645 $C$12>=0 Not Binding 7.69126645
$C$13 Green Bay Pickers Rating 11.61570711 $C$13>=0 Not Binding 11.6157071
$C$14 Houston Greasers Rating 29.05003489 $C$14>=0 Not Binding 29.0500349
$C$15 Indianapolis Ponies Rating 0.000220704 $C$15>=0 Not Binding 0.0002207
$C$16 Kansas City Indians Rating 21.56181459 $C$16>=0 Not Binding 21.5618146
$C$17 Los Angeles Pirates Rating 14.68984673 $C$17>=0 Not Binding 14.6898467
$C$18 Los Angeles Goats Rating 12.00686273 $C$18>=0 Not Binding 12.0068627
$C$19 Miami Tarpons Rating 9.082696057 $C$19>=0 Not Binding 9.08269606
$C$20 Minnesota Raiders Rating 17.23393955 $C$20>=0 Not Binding 17.2339396
$C$21 New England Volunteers Rating 7.68790325 $C$21>=0 Not Binding 7.68790325
$C$22 New Orleans Sinners Rating 24.27498564 $C$22>=0 Not Binding 24.2749856
$C$23 New York Midgets Rating 13.36636316 $C$23>=0 Not Binding 13.3663632
$C$24 New York Rockets Rating 14.44663847 $C$24>=0 Not Binding 14.4466385
$C$25 Philadelphia Hawks Rating 16.96401559 $C$25>=0 Not Binding 16.9640156
$C$26 Phoenix Sparrows Rating 9.765315699 $C$26>=0 Not Binding 9.7653157
$C$27 Pittsburgh Robbers Rating 11.03704727 $C$27>=0 Not Binding 11.0370473
$C$28 San Diego Checkers Rating 12.0133421 $C$28>=0 Not Binding 12.0133421
$C$29 San Francisco 39ers Rating 21.15470731 $C$29>=0 Not Binding 21.1547073
$C$30 Seattle Sea Lions Rating 20.20338866 $C$30>=0 Not Binding 20.2033887
$C$31 Tampa Bay Raiders Rating 4.512444896 $C$31>=0 Not Binding 4.5124449
$C$32 Washington Pigskins Rating 31.79353899 $C$32>=0 Not Binding 31.793539

11DECISION MODELLING WITH SPREADSHEETS
Variable Cells
Final Reduced
Cell Name Value Gradient
$C$5 Atlanta Eagles Rating 15.86861954 0
$C$6 Buffalo Wings Rating 14.57659441 0
$C$7 Chicago Grizzlies Rating 15.1552189 0
$C$8 Cincinnati Tigers Rating 8.381084777 0
$C$9 Cleveland Reds Rating 14.09584638 0
$C$10 Dallas Cowpokes Rating 19.71114816 0
$C$11 Denver Bravos Rating 18.38781576 0
$C$12 Detroit Leopards Rating 7.69126645 0
$C$13 Green Bay Pickers Rating 11.61570711 0
$C$14 Houston Greasers Rating 29.05003489 0
$C$15 Indianapolis Ponies Rating 0.000220704 0
$C$16 Kansas City Indians Rating 21.56181459 0
$C$17 Los Angeles Pirates Rating 14.68984673 0
$C$18 Los Angeles Goats Rating 12.00686273 0
$C$19 Miami Tarpons Rating 9.082696057 0
$C$20 Minnesota Raiders Rating 17.23393955 0
$C$21 New England Volunteers Rating 7.68790325 0
$C$22 New Orleans Sinners Rating 24.27498564 0
$C$23 New York Midgets Rating 13.36636316 0
$C$24 New York Rockets Rating 14.44663847 0
$C$25 Philadelphia Hawks Rating 16.96401559 0
$C$26 Phoenix Sparrows Rating 9.765315699 0
$C$27 Pittsburgh Robbers Rating 11.03704727 0
$C$28 San Diego Checkers Rating 12.0133421 0
$C$29 San Francisco 39ers Rating 21.15470731 0
$C$30 Seattle Sea Lions Rating 20.20338866 0
$C$31 Tampa Bay Raiders Rating 4.512444896 0
$C$32 Washington Pigskins Rating 31.79353899 0
$C$34 Home Field Advantage Rating 3.038016604 0

12DECISION MODELLING WITH SPREADSHEETS
Reference List
Hair Jr, J. F., Sarstedt, M., Ringle, C. M., & Gudergan, S. P. (2017). Advanced issues in
partial least squares structural equation modeling. saGe publications.
Tripathi, N., & Srivastava, N. (2017). Optimization problems solved by different platforms
say optimum tool box (Matlab) and Excel Solver. International Research Journal of
Engineering and Technology (IRJET), 4(09), 1284-1287.