Step-By-Step Optimization With Excel Solver              The Excel Statistical Master 
Copyright ©2011
Page 180 
For example, in cell C31 of the Excel model in the preceding image is 
the following If-Then-Else code: 
=if($C$17=1,C5,” “) 
This Excel statement copies the cash flow from C5 into C31 only 
Decision Variable cell C17 is set to 1, which indicates that this 
investment has been selected.  
This formula is copied from Cell 31 into all cells down and over to Cell 
C36. Note that Cell $C$17 is made to be an absolute reference because 
of the dollar signs. All of the copied formulas from cell C31 to Cell C36 
will depend on whether Cell C17 contains a 1 or a 0. 
The formula is also copied over and down to Cell I36. In each column, 
the absolute reference is move over. For example, all Cells from D31 to 
D36 now have absolute references on the Cell $D$17. Take a look at the 
contents of those cells in the downloadable spreadsheet containing this 
example. This concept is probably easier to understand when scrolling 
through the actual Excel spreadsheet. 
If this investment was not selected, its Decision Variable cell C17 would 
be set to 0 and nothing (“ “) would be copied into cell C31. In this way, 
only cash flows of selected investment appear once again in the 
following image: 
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Step-By-Step Optimization With Excel Solver              The Excel Statistical Master 
Copyright ©2011
Page 181 
All annual cash flows for the selected investments are summed up in the 
right column in Cells I31 to I36 as just shown. 
These combined cash flows are copied back into the right side (Cell I31 
to I36 are copied into I17 to I22) of the spreadsheet section containing 
the Decision Variable cells shown as follows: 
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Step-By-Step Optimization With Excel Solver              The Excel Statistical Master 
Copyright ©2011
Page 182 
Here is an expanded view of the left side of the previous spreadsheet: 
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Step-By-Step Optimization With Excel Solver              The Excel Statistical Master 
Copyright ©2011
Page 183 
Shown as follows is an expanded view of the right side of the Excel 
model. You can see the cash flows in I17 to I22 that have been copied 
from I31 to I36: 
The user can change the Discount Rate here and watch the spreadsheet 
calculations immediately change to reflect the new Discount Rate. The 
greater the Discount Rate, the greater that the investment risk is 
believed to be and the lower will be the NPV of the cash flows at Year 0 
of the selected investments. 
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Step-By-Step Optimization With Excel Solver              The Excel Statistical Master 
Copyright ©2011
Page 184 
The PV and NPV calculations are performed on these cash flow figures 
to attain the Objective, which is the NPV at Year 0 of all projected cash 
flows of all selected investments. 
Step 4 – List all Constraints
Step 5 – Test the Excel spreadsheet
Test the Excel spreadsheet completely before adding information to the 
Solver dialogue box. Make sure that any changes to Decision Variables 
produce the correct results in the Objective cell. 
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Step-By-Step Optimization With Excel Solver              The Excel Statistical Master 
Copyright ©2011
Page 185 
Step 6 – Insert All Data into the Solver Dialogue 
Input the Objective cell, Decision Variable cell, and all Constraints into 
the Solver dialogue box. Note that the Binary Constraint was applied to 
the 6 Yes-or-No Decision Variables. The inequality Constraints limit the 
maximum number of investments to 2 in each of Year 1 and Year 2. 
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Step-By-Step Optimization With Excel Solver              The Excel Statistical Master 
Copyright ©2011
Page 186 
All equations on the Excel spreadsheet are linear (1
order) so we can 
use the Simplex LP (Linear Programming) Solver engine for this 
optimization problem. 
Step 3 shows the completed problem with Decision Variables that have 
been optimized by the Solver to maximize the Objective while staying 
within the problem’s Constraints. 
Step-By-Step Optimization With Excel Solver              The Excel Statistical Master 
Copyright ©2011
Page 187 
Answer Report
Part 1 
 The Solver Result 
 How long Solver took to solve the problem 
 The Solver Engine that was used and the Solver Options settings 
 Where the Objective Cell was labeled in the Excel model for its 
name to appear as it does in Part 1 of the Answer Report 
Step-By-Step Optimization With Excel Solver              The Excel Statistical Master 
Copyright ©2011
Page 188 
Part 2 
 Note that the Variable Cells contain the Decision Variables 
 Note where the labels for each Decision Variable are placed in 
the Excel model so that the Decision Variable’s name will appear 
here in Part 2 of the Answer Report as it does 
 Note the type of variable  - Either Continuous or Integer (Integer, 
Binary, or Alldifferent) 
 Note the Before and After values of each Decision Variable 
Step-By-Step Optimization With Excel Solver              The Excel Statistical Master 
Copyright ©2011
Page 189 
Part 3 
 Note how each Constraint is labeled in the Excel model in order 
for the Constraint’s name to appear here in Part 3 of the Answer 
Report as it does 
 Note which Constraints are binding (had their limits hit) and which 
 Note how much slack is still available in any Constraint that has 
not had its limit hit. 
 Note any Integer Constraints (Integer, Binary, Alldifferent) 
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