VIPSolutionsGive step-by-step solution with explanation and final answer: 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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Give step-by-step solution with explanation and final answer: 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 22:23:22
Asked by: Shadab
Created at: 2025-09-17 22:23:22
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# Amusement Park Breakeven
## Given Data
- Fixed costs (FC): \$500,000 per
- **Current scenario:**
- Entry fee (P):50
- Average variable cost (AVC): \$10 per visitor
- **Proposed scenario:**
- Entry fee: \$60
Variable cost: \$15 per visitor
---
## (a) Breakeven Point (Current)
### **Step 1: Breakeven Formula**
\[
\text{Breakeven Point (Q)} = \frac{\text{Fixed Costs (FC)}}{\text{Price (P)} - \text{Average Variable Cost (AVC)}}
\]
### **Step 2: Plug in Values**
\[
Q = \frac{500{,}000}{50 - 10} = \frac{500{,}000}{40} = 12,500
\]
### **Step 3: Interpretation**
- **Breakeven point:** The park must have **12,500 visitors per month** to cover its costs.
---
## (b) New Breakeven Point (with higher price and cost)
- New entry fee: \$60
- New AVC: \$15
### **Step 1: Use Breakeven Formula**
\[
Q = \frac{500{,}000}{60 - 15} = \frac{500{,}000}{45} \approx 11,111.11
\]
### **Step 2: Round as needed**
- **Breakeven point:** The park now needs about **11,112 visitors per month** (rounded up to the next whole visitor).
---
## (c) Profitability at 25,000 Visitors (New Scenario)
- Visitors per month: 25,000
- Entry fee: \$60
- AVC: \$15
- FC: \$500,000
### **Step 1: Calculate Total Revenue (TR)**
\[
TR = 25,000 \times 60 = \$1,500,000
\]
### **Step 2: Calculate Total Variable Cost (TVC)**
\[
TVC = 25,000 \times 15 = \$375,000
\]
### **Step 3: Calculate Total Cost (TC)**
\[
TC = FC + TVC = 500,000 + 375,000 = \$875,000
\]
### **Step 4: Calculate Profit**
\[
\text{Profit} = TR - TC = 1,500,000 - 875,000 = \$625,000
\]
### **Step 5: Interpretation**
- The park will **still be profitable**, earning \$625,000 per month at 25,000 visitors.
---
## **Summary Table**
| Scenario | Breakeven Visitors | Actual Visitors | Profit/Loss |
|------------------|-------------------|-----------------|----------------------|
| (a) Original | 12,500 | 42,000 | Profitable |
| (b) After Change | 11,112 | --- | --- |
| (c) After Change | 11,112 | 25,000 | Profit: \$625,000 |
---
## **Final Answers**
**a.** Breakeven point is **12,500 visitors per month**.
**b.** New breakeven point is **11,112 visitors per month**.
**c.** With 25,000 visitors at the higher price and cost, the park **will still be profitable** (profit = \$625,000 per month).
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