Math Help

Optimization

Optimization applications involve finding the maximum or minimum of a function.

This function is sometimes called the “objective” or “cost” function, and may be

subject to one or more constraints. The objective may be many different things such as

finding the minimum distance between a curve and a given point (see example 1) or

the length of the longest ladder that will fit at a corner (see example 2).

Construction of a clear diagram is generally the first (and recommended step).
It should show the variables in the diagram.

The table below details the strategy in analyzing optimization applications

Draw a clear picture of the situation assigning names to each variable.

Identify the unknown quantity (objective function), to be optimized.

Express any constraints limiting the objective function.

Combine the objective function subject to constraints to express the

objective function in terms of only one independent variable.

The first derivative of the objective function must equal zero for a

maximum or minimum.

Solve for each variable and substitute into the objective function.