To determine whether purchasing the monthly membership is a better option than paying per visit, we can set up the equations based on your usage.
Option A: Pay per visit.
The cost function is:
Option B: Monthly membership.
The cost function is:
Now, we can compare the two cost functions to find the break-even point, which is when both costs are equal:
To solve for
-
Subtract
from both sides: -
Divide by 5:
This means that if you plan to visit the trampoline park more than 6 times in a month, the membership option will be cheaper.
-
If you visit 6 times:
- Option A:
- Option B:
(break-even)
- Option A:
-
If you visit 7 times:
- Option A:
- Option B:
( membership is cheaper)
- Option A:
-
If you visit 5 times:
- Option A:
- Option B:
(pay per visit is cheaper)
- Option A:
Given this analysis, it would make sense to buy the membership if you plan to visit more than 6 times in a month. If you anticipate using the trampoline park less than or equal to 6 times, then it would be more cost-effective to pay the regular fee of $9 per visit.