Concept 5

Revise a model when assumptions change or new constraints are introduced.

Revise only the part of the model that the new condition actually changes.

Core Idea

When the situation changes, update the part of the model that the new condition actually affects.

Understanding

Rule: Change only the part the new condition affects.

Keep the pieces that still match the situation.
Update the constant if a starting fee changes or disappears.
Update the coefficient if the rate changes.
Add an inequality or piecewise rule if the new condition adds a cap or minimum.

Step by Step

Label what each term in the original model represents.
Identify which quantity changes under the new condition.
Rewrite only the affected term or constraint, then re-read the new model in context.

Misconceptions

Changing every number in the equation instead of tracing which quantity the new condition actually changes.
Leaving an old fee or rate in the model even after the problem says it was removed or replaced.
Missing that a new maximum or minimum may require an inequality instead of another equation.

Question

Worked Example

A bike rental company originally uses $𝐶 = 18 + 4 ℎ$ , where $𝐶$ is the cost in dollars and $ℎ$ is the number of hours rented. A new plan removes the $18 starting fee but raises the hourly rate to $6 per hour. Which equation models the new plan?

Select an answer to see the explanation