1. Determine what is to be maximized or minimized.

2. Write an algebraic relationship defining the quantity being maximized or minimized.

3. Write any other appropriate algebraic relationships.

4. Express the quantity to be maximized or minimized as an equation in one variable

5. Sketch a graph of the above relationship with particular emphasis on the domain of the function.

6. Determine critical values in the domain to determine likely places for maxima and minima.

7. Determine the maximum or minimum value of the function over the appropriate domain.
    Be sure to check for absolute maxima and minima, not just relative maxima and minima.