Put these steps for solving an applied optimization problem in the correct order. (It may help to also look at the link to the examples or watch the first few minutes of the first video.)
- If possible, draw a picture!
- Label your picture, assigning variables for quantities that can change, and filling in constant values for quantities that will not change.
- Find the domain of the [new] objective equation.
- Create or identify the equation to be maximized or minimized and the equation that describes the constraint.
- Find the maximum or minimum using calculus. (Technically we're finding an absolute max/min so don't forget to check at the endpoints, but in these problems it very often occurs at a local max/min in the domain and in many problems there's only one possibility.)
- Verify your answer using either the First Derivative Test or the Second Derivative Test.
- Be sure you have answered the question that the problem is asking!
- Use the constraint equation to rewrite the objective equation so that it has only one independent variable.