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Step-By-Step Optimization With Excel Solver              The Excel Statistical Master 
Copyright ©2011 http://excelmasterseries.com/New_Manuals.php
Page 220 
The first step is to eyeball the data and estimate what general type of 
curve these data points most likely fit to. In this case the data points 
appear to a graph the has a diminishing y value for an increasing x 
value. The formula for such a curve would have this general form: 
Y = A1 + A2 * X
B1
Sales = A1 + A2 * (Number of Ads Running)
B1
We can use the Excel Solver to solve for A1, A2, and B1. We need to 
arrange the data in this format as inputs into the Excel Solver as follows: 
The preceding image shows the Excel model after it has already been 
solved. By “solved,” we mean in this case that the Solver has calculated 
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Step-By-Step Optimization With Excel Solver              The Excel Statistical Master 
Copyright ©2011 http://excelmasterseries.com/New_Manuals.php
Page 221 
the Decision Variable values (in the green cells B3 to B5) that minimize 
the Objective. 
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Step-By-Step Optimization With Excel Solver              The Excel Statistical Master 
Copyright ©2011 http://excelmasterseries.com/New_Manuals.php
Page 222 
This table shows the arrangement of data and the calculations. Here we 
have created an Excel model based upon our model of: 
Sales = A1 + A2 * (Number of Ads Running)
B1
One example of this formula in action is explained for Cell E12. We are 
listing the variable that we are solving for (A1, A2, and B1) in cells B3 to 
B5. In Solver language, these solves that we are changing are called 
Decision Variables. 
We arbitrarily set our Decision Variables for: 
A1 = 100 
A2 = 100 
B1 = 0.05 
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Step-By-Step Optimization With Excel Solver              The Excel Statistical Master 
Copyright ©2011 http://excelmasterseries.com/New_Manuals.php
Page 223 
The Excel model shown before running the Solver as follows: 
Before Running Solver
We now take the difference between the actual number of sales and the 
number of sales predicted by our model with our arbitrary settings for the 
Decision Variables. The square of each difference is taken and then all 
squares are summed up in the yellow Objective Cell C14.  
We are trying to find the settings for the Decision Variables that will 
minimize the sum of the squares of the differences. In other words, we 
are trying to find A1, A2, and B1 that will minimize the number in cell 
G14. 
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Step-By-Step Optimization With Excel Solver              The Excel Statistical Master 
Copyright ©2011 http://excelmasterseries.com/New_Manuals.php
Page 224 
Bring up the Excel Solver and the following blank Solver dialogue box 
comes up: 
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Step-By-Step Optimization With Excel Solver              The Excel Statistical Master 
Copyright ©2011 http://excelmasterseries.com/New_Manuals.php
Page 225 
The Solver dialogue box has the following 4 parameters that need 
to be set: 
1) The Objective Cell
– This is the target cell that we are either 
trying to maximize, minimize, or achieve a certain value.  
2) Minimize or Maximize the Target
, or attempt to achieve 
a certain value in the Objective cell. 
3) Decision Variables
– A set of variables that will be changed 
by the Excel Solver in order to optimize the target cell. 
4) Constraints
– These are the limitations that the problem 
subjects the Solver to during its calculations 
Once again, here is the data table for Solver inputs as follows: 
Step-By-Step Optimization With Excel Solver              The Excel Statistical Master 
Copyright ©2011 http://excelmasterseries.com/New_Manuals.php
Page 226 
Objective:
We are trying to minimize yellow Objective Cell G14, the sum of the 
square of differences between the actual and predicted sales. 
Step-By-Step Optimization With Excel Solver              The Excel Statistical Master 
Copyright ©2011 http://excelmasterseries.com/New_Manuals.php
Page 227 
Decision Variables:
We are changing A1, A2, and B1 (green cells B3 to B5) to minimize the 
Objective Cell G14. The Decision Variables are therefore Cells B3 to B5. 
Constraints: 
There are none for this curve-fitting operation. 
Selection of Solving Method: GRG Nonlinear
The GRG Nonlinear method is used when the equation producing the 
objective is not linear but is smooth (continuous). Examples of smooth 
nonlinear functions in Excel are: 
=1/C1, =Log(C1), and =C1^2  
These functions have graphs that are curved (nonlinear), but have no 
breaks (smooth) 
Our sales equation appears to be smooth and non-linear: 
Sales = A1 + A2 * (Number of Ads Running)
B1
Step-By-Step Optimization With Excel Solver              The Excel Statistical Master 
Copyright ©2011 http://excelmasterseries.com/New_Manuals.php
Page 228 
The completed Solver dialogue box: 
Note that we do not want to check the option Make Unconstrained 
Variables Non-Negative. It is possible that coefficients of the regression 
equation will be negative. It turns out that 1 of the regression coefficients 
actually is negative. 
Step-By-Step Optimization With Excel Solver              The Excel Statistical Master 
Copyright ©2011 http://excelmasterseries.com/New_Manuals.php
Page 229 
If we now hit the Solve button, we get the following result, which in this 
case is the set of Decision Variables that minimize the Objective: 
After Running Solver 
We actually ran Solver twice to obtain this result. Often the GRG 
Nonlinear method will produce different solutions on successive Solver 
runs. The result of each run GRG Nonlinear run on a nonlinear problem 
depends on the “starting point” that the Solver selects. It is often a good 
idea to run the GRG Nonlinear method several times in a row to find the 
most optimal solution. 
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