**What is the Objective Function?**

The objective of a linear programming problem will be to maximize or to minimize some numerical value. This value may be the expected net present value of a project or a forest property; or it may be the cost of a project; it could also be the amount of wood produced, the expected number of visitor-days at a park, the number of endangered species that will be saved, or the amount of a particular type of habitat to be maintained. Linear programming is an extremely general technique, and its applications are limited mainly by our imaginations and our ingenuity.

The objective function indicates how much each variable contributes to the value to be optimized in the problem. The objective function takes the following general form:

where

c_{i}_{}= the objective function coefficient corresponding to thei^{th}variable, and

X= the_{i}i^{th}decision variable. \1

The coefficients of the objective function indicate the contribution
to the value of the objective function of one unit of the corresponding
variable. For example, if the objective function is to maximize
the present value of a project, and *X _{i }* is
the

Note that the way the general objective function above has been written implies that each variable has a coefficient in the objective function. Of course, some variables may not contribute to the objective function. In this case, you can either think of the variable as having a coefficient of zero, or you can think of the variable as not being in the objective function at all.

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