Ettenheim village is considering building a town swimming pool. The annual facility cost would be $200,000. Staff salaries for the pool, which would only be open during the summer would be $75,000. Other fixed cost would be $20,000 a year. There are other expenses of $50 per person per season.
Marketing studies suggest that the village residents would be willing to spend $150 a year for an individual membership and $300 for family membership. On average families in the village have 3 people. How many members will have to join each year to make the pool cover its cost. Assume that 75% of the memberships are family memberships
Let N be the number of members. The annual revenue from memberships will be
(0.75N)x150 + (0.25N)x300 = 187.5 N
Add up the annual costs, which look to me like
295,000 + 50 N,
set that equal to 187.5 N and solve for N. That will give you the break-even value of N.
To determine the number of members that need to join each year to cover the cost of the pool, we need to calculate the total revenue generated by memberships and compare it to the total cost of operating the pool.
1. Calculate the cost of operating the pool:
- Annual facility cost: $200,000
- Staff salaries: $75,000
- Other fixed costs: $20,000
Total cost = $200,000 + $75,000 + $20,000 = $295,000
2. Calculate the revenue generated per member:
- Individual membership fee: $150 per year
- Family membership fee: $300 per year (covers 3 people)
3. Calculate the number of family memberships:
- Assume that 75% of the memberships are family memberships
- Average number of people per family membership: 3
Number of family memberships = 75% of the total memberships
4. Calculate the revenue generated by family memberships:
- Number of family members = Number of family memberships * Average number of people per family membership
- Revenue from family memberships = Number of family memberships * Family membership fee
5. Calculate the revenue generated by individual memberships:
- Number of individual memberships = Total memberships - Number of family memberships
- Revenue from individual memberships = Number of individual memberships * Individual membership fee
6. Calculate the total revenue generated by memberships:
- Total revenue = Revenue from family memberships + Revenue from individual memberships
7. Finally, solve for the number of memberships needed to cover the cost by setting the total revenue equal to the total cost:
- Total revenue = Total cost
- Total memberships * (Revenue per membership) = Total cost
Now, you can follow these steps and calculate the number of members required to cover the cost of the pool.