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When should you use Solver?

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Okay, I’ll be straight with you: Solver is a powerful tool that most Excel users don’t need. It would be overkill, for example, to use Solver to compute net profit given fixed revenue and cost figures. Some problems, however, require nothing less than the Solver approach. These problems cover many different fields and situations, but they all have the following characteristics in common:

 They have a single objective cell (also called the target cell) that contains a formula you want to maximize, minimize, or set to a specific value. This formula could be a calculation such as total transportation expenses or net profit.

 The objective cell formula contains references to one or more variable cells (also called unknowns or changing cells). Solver adjusts these cells to find the optimal solution for the objective cell formula. These variable cells might include items such as units sold, shipping costs, or advertising expenses.

 Optionally, there are one or more constraint cells that must satisfy certain criteria. For example, you might require that advertising be less than 10 percent of total expenses, or that the discount to customers be an amount between 40 and 60 percent.

For example, Figure 2-11 shows a worksheet data model that’s all set up for Solver. The model shows revenue (price times units sold) and costs for two products, the profit produced by each product, and the total profit. The question to be answered here is this: How many units of each product must be sold to get a total profit of $0? This is known in business as a break-even analysis.


FIGURE 2-11: The goal for this data model is to find the break-even point (where total profit is $0).

That sounds like a straightforward Goal Seek task, but this model has a tricky aspect: the variable costs. Normally, the variable costs of a product are its unit cost times the number of units sold. If it costs $10 to produce product A and you sell 10,000 units, the variable costs for that product are $100,000. However, in the real world, such costs are often mixed up among multiple products. For example, if you run a joint advertising campaign for two products, the costs are borne by both products. Therefore, this model assumes that the costs of one product are related to the units sold of the other.

Here, for example, is the formula used to calculate the costs of the Inflatable Dartboard (cell B8):

=B7 * B4 – C4

In other words, the variable costs for the Inflatable Dartboard are reduced by one dollar for every unit sold of the Dog Polisher. The latter’s variable costs use a similar formula (in cell C8):

=C7 * C4 – B4

Having the variable costs related to multiple products puts this data model outside of what Goal Seek can do, but Solver is up to the challenge. Here are the special cells in the model that Solver will use:

 The objective cell is C14; the total profit and the target solution for this formula is 0 (that is, the break-even point).

 The changing cells are B4 and C4, which hold the number of units sold for each product.

 For constraints, you might want to add that both the product profit cells (B12 and C12) should also be 0.

Excel Data Analysis For Dummies

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