**What are Linear Functions?**

All of the equations in a linear program must, by definition, be linear. A linear function has the following form:

In general, the *a*'s are called the *coefficients*
of the equation; they are also sometimes called *parameters*.
The important thing to know about the coefficients is that they
are fixed values, based on the underlying nature of the problem
being solved. The *x*'s are called the *variables*
of the equation; they are allowed to take on a range of values
within the limits defined by the constraints. Note that it is
not necessary to always use x's to represent variables; any label
could be used, and more descriptive labels are often more useful.

Linear equations and inequalities are often written using summation notation, which makes it possible to write an equation in a much more compact form. The linear equation above, for example, can be written as follows:

Note that the letter *i* is an *index*, or counter,
that starts in this case at 1 and runs to *n*. There is a
term in the sum for each value of the index. Just as a variable
does not have to be specified with a letter *x*, the index
does not have to be a letter *i*. Summation notation will
be used a lot in the rest of this chapter and in all of the remaining
chapters. You will need to become adept at interpreting it.

Back to Section 1