Before we continue, you should check to see that Solver is installed on your version of Excel.

Navigate to the add-ins menu, and make sure that Solver Add-in has a check in the box next to it.

You should then be able to find Solver in the Data tab.

If you’re able to see Solver in the Data tab like in the screenshot above, you should be all set to use Solver in Excel.

To understand how to use Solver in Excel, you should know the group of cells that the add-in works with:

• Decision Variable Cells: The values in the variable cells are adjusted by Solver when solving a problem.
• Constraint Cell: Provides Solver with the restrictions, or limits on the values that it has to work with in order to produce a result.
• Objective Cell: Solver provides the optimal value depending on the criteria provided in the Objective Cell. This cell must contain a formula.

Before you start to use Solver, you will want to have a spreadsheet set up with a problem that you want to solve. For demonstration purposes we will work with a spreadsheet that is trying to determine how many of four different types of “Widgets” to manufacture in order to maximize profits.

We will assume that each Widget produces the following profits:

• Widget A: $25
• Widget B: $35
• Widget C: $45
• Widget D: $55

Assuming there were no constraints, and we could manufacture and sell Widget D just as easily as the other Widgets, we should drop Widgets A-C and just focus on Widget D.

However in real life there are constraints such as time to produce, availability of materials, etc.

Let’s also assume the following constraints for each Widget:

• Widget A Requires:
  • Part A: 4
  • Part B: 6
  • Time (hours): 0.25 (15 minutes)
• Widget B Requires:
  • Part A: 6
  • Part B: 5
  • Time (hours): 0.25 (15 minutes)
• Widget C Requires:
  • Part A: 4
  • Part B: 8
  • Time (hours): 0.5 (30 minutes)
• Widget D Requires:
  • Part A: 6
  • Part B: 10
  • Time (hours): 0.5 (30 minutes)

We also have a maximum of 17,000 Part A, 50,000 Part B, and 2,000 hours of labor.

What we are looking to do is solve the following equation, where Y_A is the quantity of Widget A, Y_B is the quantity of Widget B, and so on.

Maximize: 25 Y_A + 35 Y_B + 45 Y_C + 55 Y_D

Subject to these constraints:

Part A: 4 Y_A + 6 Y_B + 4 Y_C + 6 Y_D <= 17,000
Part B: 6 Y_A + 5 Y_B + 8 Y_C + 10 Y_D <= 50,000
Time: 0.25 Y_A + 0.25 Y_B + 0.5 Y_C + 0.5 Y_D <= 2,000

Additionally, another constraint is you can’t build a negative number of any of the Widgets, so:

Y_A + Y_B + Y_C + Y_D >= 0

Set-up Your Spreadsheet With Data

We can then build a spreadsheet with this information:

In the spreadsheet all the numbers, other than the numbers in column G, were manually entered. There are four cells with formulas:

• G5: =SUMPRODUCT(C3:F3,C4:F4) – Note this is the same as saying =C3*C4+D3*D4+E3*E4+F3*F4.
• G8: =SUMPRODUCT(C8:F8:$C$4:$F$4) – In this formula, we add the $ signs to keep the reference to cells C4:F4 static when we eventually copy the formula to other cells.
• G9-G10: Copy the formula from G8 down to G9 and G10. Since we used the $ signs in the formula in G8, the formula in G9 and G10 will retain the references to cells C4:F4 (because this part had the $ signs), but will update itself to reference C9:F9, and C10:F10 (since this part did not have $ signs).

Use Solver to Maximize Profits:

Now, to find out the maximum profit, we are going to let Solver run through the scenario and provide us with an answer. First we need to tell Solver what we are trying to do.

• On the Data tab, click on Solver.
• Click in the Set Objective field and type $G$5, or click on cell G5. This tells Solver which cell we want to optimize.
• The To option should be set to Max. This tells Solver that we want to maximize the value in cell G5.
• In the By Changing Variable Cells box, type $C$4:$F$4, or highlight the range C4:F4 with your mouse. This tells Solver which cells should change in order to maximize the value in cell G5.
• Next to the Subject to Constraints box click the Add button. Here we will provide the constraints that we described in the math formula above.
  • We want the resources to be limited by the quantities we have available, so in the Cell Reference box (left side), enter $G$8:$G$10, or select the range G8:G10 with your mouse.
  • The dropdown box (middle) should be set to <=.
  • The Constraint box (right side) should be set to the maximum quantities available, which in our case is $H$8:$H$10.
  • Click OK.
• If we had additional constraints to enter, we could do so by clicking the Add button. In this case we want to make sure the Units to produce are not negative, we could enter a new constraint of $C$4:$F$4 >= 0.
• Since all of our variables are constrained, it won’t change the outcome if you check or uncheck the box for Make Unconstrained Variables Non-Negative.
• Click Solve.

Solver will run through the problem and provide the optimal number of each Widget type to produce in order to maximize profits. You should see a message saying that “Solver found a solution”.

In this scenario, in order to maximize profits we need to produce 3,500 of Widget C, 500 of Widget D, and none of Widgets A or B.

Find Ways to Further Maximize Profits:

If we want to generate an Answer report, click on Answer under the Reports section in the Solver Results window. Solver will create an Answer Report tab to the left of the tab you are working on.

The Answer Report will show you the original and final values of the objective and variable cells. It will also list out the resources that prevented Solver from further maximizing our profits.

In this case, Part A and Time were both fully used up. In the report their status is “Binding”, with a slack of 0. Part B was the only resource that was not binding, as there were 17,000 units left over.

In the real world we could use this information to try to determine if we could possibly acquire more of Part A, and hire more employees to further maximize the profits.

If this wasn’t a possibility, we could see if there was something else we could make with the 17,000 remaining units of Part B.

Other Ways to Use Solver in Excel:

We just ran through a simple scenario to maximize the profit of a widget manufacturer. However the usage of Solver is not limited to producing widgets.

You can use Solver in Excel to help allocate money to certain investments, purchasing real-estate, or scheduling staff at a multi-location business.

Do you use Solver in Excel? Let’s hear about how you use it in the comments.

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The question I want to solve is: if I sell all the shares that have produced a gain, how many of the shares should I sell at a loss in order to offset the gains, and the resulting taxes?

To do this, I set up my spreadsheet like the one below:

Note: these are not the actual amounts I used in my own personal situation. They are only provided for illustration purposes.

Download the example file here.

In cell F8 (labeled “Losses to Break Even” in cell E8), I have the following formula: =(F9*B2)-(F9*D2), which I want to equal the total gains amount, of $1,936.10.  Right now it is showing a zero value because I haven’t determined how many shares need to be sold at a loss to equal the gains.

To do this, select cell F8, then click Tools | Goal Seek.  In the box that pops up, enter the following:

• Set cell: Keep as F8.  If it isn’t F8, enter F8 here.
• To value: Enter 1,936.10, as this is the value we wish to set the losses to.
• By changing cell: Enter cell F9, as you want to determine how many shares need to be sold in order to break even.
• Click OK

The result will tell you that you should sell 43.54 shares in order to break even.

For more information on Excel’s Goal Seek feature, take a look at the post Goal Seek to Solve a Problem.

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First, some background on what it does.  Goal Seek is essentially the answer to every middle school aged kid’s math test word problem.  It is best used when you know the answer to the problem you’re trying to solve, but don’t know all the inputs.

For example, a simple word problem might be “You have 432 sheets of paper to give out to a class of 36 students.  How many sheets of paper does each student get.”  Well you know that 36 multiplied by something will give you 432, but you don’t know what that number is.  You could divide 432 by 36 to get the answer, but let’s assume that isn’t possible right now.  With Goal Seek, you need several things:

• An answer expressed as a formula, in this case 432 is equal to 36 times something.  Don’t worry, the result of the formula doesn’t have to equal 432 yet.  That’s the magic of Goal Seek.
• You need one part of the equation, in this case 36.

To start, type the following into your spreadsheet in the cells indicated.

Next, open Goal Seek (Tools | Goal Seek, or Data tab on the Excel 2007 ribbon | What If Analysis | Goal Seek).

You are now going to be asked for three things. 

1. Set Cell: this is the reference to the cell that contains your formula, in which you want Excel to produce your answer of 432.  In our example it should be A3.  Note: the Set Cell MUST contain a formula or function.
2. To Value: this is the value you want in your Set Cell (A3).  The value here should be 432.
3. By Changing Cell: Since we know that the formula in cell A3 is correct, and the value of 36 in cell A1 is correct, we want Excel to produce the answer of 432 by changing cell A2.  Type A2 in this box.  Note: the Changing Cell MUST contain a value.
4. Click OK.

After clicking OK, Excel will attempt to find a solution to the equation.  Once it does, it will enter the missing number in cell A2 and your formula should now equal 432.

Obviously this is a basic example, and doesn’t use Goal Seek’s capabilities to their fullest extent.  Let’s take another example that looks at a company’s sales by product to get their desired level of revenue.

XYZ Company makes four different products, Product A, Product B, Product C, and Product D.  The company can produce 1,000, 750, 500, and 100 of each product respectively.  The products also sell for $15, $20, $35, and $50 respectively.  Their maximum revenue for products produced that month, therefore is as follows:

Now say the company feels that their underdog, Product D, could be producing much more.  They also want their revenues to be 60,000.  How many more of Product D will they need to produce?

To figure this out, run Goal Seek just like before, except this time, the “Set Cell” is cell D6, “To Value” is 60,000, and the “By Changing Cell” is cell B5.  After clicking OK, you’ll notice that Excel has changed the value in cell B5 to 250, indicating that you will need to increase production of Product D to 250 units from 100 in order to have revenues of $60,000, assuming everything else remains the same.

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