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ALGEBRAIC FORMULATION

Formulation

A formal, algebraic statement of a constrained optimization problem.

The text description of the problem is fine for communicating a general understanding, but in order to address the problem using optimization we need to develop a formal algebraic description, called a formulation. A formulation contains explicit definitions of the decision variables, an algebraic expression of the objective function, and algebraic statements of the constraints. This is not as hard as it sounds, but it is a crucial step if you hope to develop a high-quality spreadsheet model that Solver can successfully solve.

A diagram of the situation can help to structure the problem so that the algebraic formulation can be written down more easily. A well-constructed diagram is also a valuable communication tool. In this situation, three resources are combined to produce two products. Specific amounts of each resource are needed, and each product generates a known profit. See Figure B-2 for one way to show this. One of the important points is that the total amount of each resource available must be shared between the two products (assuming both are to be produced).

A diagram, coupled with a text-based formulation, often serves as a valuable stepping stone to a formal algebraic formulation. In this situation, a text-based formulation can be stated as follows:

Text-Based Formulation ...

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