An investment club has been able to purchase 12,000 m squared of land for an establishment Malaysia Park the park will have a variety of relaxation points including a swimming pool and then a parking area the swimming pool will be rectangular measuring from it as by 3 m surrounded by a deck of uniform with better area of the swimming pool and the deck will be 172m squared the space of 400 m squared is to be reserved for parking a car requires 5 m squared and a van requires 20 m squared of space the car park attendant can only handed 50 vehicles each car will be charged 4,000 to be charged 5000 to serve with a Visa bitter when asha is enough to attend at most 10 visitors and for every addition of five visitors and extra usher will be required

Let's break down the details provided to solve the problem:

### 1. **Land Allocation**
   - **Total Land Area**: 12,000 m²
   - **Swimming Pool**: A rectangular pool measuring \( l \times w \), with \( l = l \) and \( w = 3 \) meters (you didn’t specify \( l \), so let's use \( l \)).
   - **Deck**: Surrounds the pool with a uniform width, and the total area of the pool and the deck combined is 172 m².
   - **Parking Area**: 400 m² reserved for parking.

### 2. **Swimming Pool and Deck Area Calculation**
   - **Area of the Pool**: \( \text{Area of the pool} = l \times 3 \) m².
   - **Area of the Deck**: Total area (pool + deck) = 172 m².
   
   Let's denote the uniform width of the deck as \( d \). The total dimensions of the pool and deck together would be \( (l + 2d) \times (3 + 2d) \).

   The area of the pool and deck combined:
   \[
   (l + 2d) \times (3 + 2d) = 172 \quad \text{and} \quad l \times 3 + \text{Area of the Deck} = 172
   \]

### 3. **Parking Area and Capacity**
   - **Total Parking Area**: 400 m²
   - **Space Requirements**:
     - Car: 5 m² per car.
     - Van: 20 m² per van.
   - The number of vehicles that can fit in 400 m²:
     - \( x \) cars and \( y \) vans, so:
     \[
     x + y \leq 50
     \]
     \[
     5x + 20y \leq 400
     \]

### 4. **Revenue Calculation**
   - **Charges**:
     - Car: 4000 per car.
     - Van: 5000 per van.

   The total revenue \( R \) can be calculated as:
   \[
   R = 4000x + 5000y
   \]

### 5. **Staffing Requirements**
   - **Maximum Number of Visitors per Usher**: 10 visitors.
   - For every additional 5 visitors, an extra usher is required.

   Let's assume each vehicle brings a certain number of visitors, denoted as \( v \). If the total number of vehicles \( (x + y) \) is known, and each vehicle brings \( v \) visitors, then:
   - Total visitors \( V = v \times (x + y) \).
   - Number of ushers required:
   \[
   \text{Number of Ushers} = 1 + \left\lceil \frac{V - 10}{5} \right\rceil
   \]

### Summary of the Problem and Equations:
- **Swimming Pool and Deck Area**:
   \[
   (l + 2d) \times (3 + 2d) = 172
   \]
- **Parking Space**:
   \[
   5x + 20y \leq 400 \quad \text{and} \quad x + y \leq 50
   \]
- **Revenue**:
   \[
   R = 4000x + 5000y
   \]
- **Staffing**:
   \[
   \text{Number of Ushers} = 1 + \left\lceil \frac{V - 10}{5} \right\rceil
   \]

Would you like me to go through specific calculations, such as solving for \( l \) and \( d \) for the pool area or determining the optimal mix of cars and vans to maximize revenue?

### 5 Related Questions:
1. How do you solve for the dimensions of the pool and deck given the area constraints?
2. What is the maximum revenue you can achieve with the given parking constraints?
3. How do the number of vehicles affect the number of ushers required?
4. What combination of cars and vans optimizes the use of the parking space?
5. How would changing the parking area size affect the overall plan?

**Tip**: When determining staffing requirements, it’s useful to consider the peak visitor numbers and how changes in vehicle distribution impact the visitor count.

Explore how to allocate land effectively for Malaysia Park, including calculating swimming pool and deck areas, parking space requirements, revenue generation from vehicle charges, and staffing needs based on visitor counts. Suitable for advanced high school students and beyond.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation