To create optimization models with calculus, we use a simple step-by-step method. This method helps us connect real-world issues to math. The main aim of optimization is to find the highest or lowest value of a function. This is often called the objective function.

Here’s how we do it:

1. Define the Problem:
   Figure out what you want to improve. For example, you might want to make the most profit or spend the least amount of money.

2. Formulate the Function:
   Write down your goal using math. This usually means creating a function, like $f(x)$, that shows how the thing you care about depends on one or more factors.

3. Determine Constraints:
   In many situations, there are limits on what you can change. These limits can be written as equations or inequalities that show what solutions are possible.

4. Apply Derivatives:
   To find the best values, calculate the derivative, $f'(x)$, and set it to zero. This helps you find points where the function changes. Check the second derivative, $f''(x)$, to see if those points are where the function hits a high or low point.

5. Solve for Variables:
   Use the derivatives, along with any limits you found, to figure out what values for your factors will give you the best results for your goal.

6. Verify and Interpret:
   Finally, look at your answers and see if they make sense in the real world. Make sure they fit the original problem you started with.

This method captures how calculus helps us solve optimization problems. It gives a clear way to handle complicated real-life situations using math tools.