VIPSolutions2-19 An amusement park faces large fixed costs of $500,000 per month and low average variable costs of $10 per visitor. It charges all visitors a flat entry fee of $50 for unlimited rides. a. What is the breakeven point for this park? b. The park currently has 42,000 visitors a month and proposes to raise its entry fee to $60 per person in order to cover the cost of a new Harry Potter–themed ride. What is the new breakeven point if the variable cost increases to $15 per visitor? c. If the park now receives 25,000 visitors a month because of the increase in entrance fee in Part (b), will the park still be profitable? (2.2)
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2-19 An amusement park faces large fixed costs of $500,000 per month and low average variable costs of $10 per visitor. It charges all visitors a flat entry fee of $50 for unlimited rides. a. What is the breakeven point for this park? b. The park currently has 42,000 visitors a month and proposes to raise its entry fee to $60 per person in order to cover the cost of a new Harry Potter–themed ride. What is the new breakeven point if the variable cost increases to $15 per visitor? c. If the park now receives 25,000 visitors a month because of the increase in entrance fee in Part (b), will the park still be profitable? (2.2)
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Asked by: Shadab
Created at: 2025-09-17 22:23:09
Asked by: Shadab
Created at: 2025-09-17 22:23:09
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# Amusement Park Cost Analysis
## a. Breakeven Point (Original Situation)
**Given:**
- Fixed Costs (FC): \$500,000/month
- Average Variable Cost (AVC): \$10/visitor
- Entry Fee (Price, \(P\)): \$50/visitor
**Breakeven Point Formula:**
\[
\text{Breakeven quantity} = \frac{\text{Fixed Costs}}{\text{Price per visitor} - \text{Variable Cost per visitor}}
\]
**Calculation:**
\[
\text{Breakeven quantity} = \frac{500{,}000}{50 - 10} = \frac{500{,}000}{40} = 12{,}500\ \text{visitors}
\]
---
## b. New Breakeven Point (After Fee Increase & Cost Change)
**Given:**
- New Entry Fee (\(P\)): \$60/visitor
- New AVC: \$15/visitor
- Fixed Costs: \$500,000/month
**Calculation:**
\[
\text{Breakeven quantity} = \frac{500{,}000}{60 - 15} = \frac{500{,}000}{45} \approx 11{,}111.11\ \text{visitors}
\]
---
## c. Profitability at 25,000 Visitors (After Changes)
**Given:**
- Visitors: 25,000/month
- Entry Fee: \$60/visitor
- Variable Cost: \$15/visitor
- Fixed Costs: \$500,000/month
**Total Revenue:**
\[
\text{TR} = 25{,}000 \times 60 = 1{,}500{,}000
\]
**Total Variable Cost:**
\[
\text{TVC} = 25{,}000 \times 15 = 375{,}000
\]
**Total Cost:**
\[
\text{TC} = \text{Fixed Cost} + \text{TVC} = 500{,}000 + 375{,}000 = 875{,}000
\]
**Profit:**
\[
\text{Profit} = \text{TR} - \text{TC} = 1{,}500{,}000 - 875{,}000 = 625{,}000
\]
**Conclusion:**
*Yes, the park will still be profitable with 25,000 monthly visitors after the price and cost increase.*
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