The table below shows the number of sales associates and the average number of customers per day visiting a store at a company's two department stores. The company is planning to add a new sales associate to one of the stores.
Shopping Mall Location	Number of Sales Associates	Average Number of Customers Per Day
Summer Hill Galleria	561	5,589
Seaside Mall Galleria	675	5,785
Determine the relative unfairness of an apportionment that gives Summer Hill the new employee. (Round your answer to the nearest thousandth.)
 
Incorrect: Your answer is incorrect.
Determine the relative unfairness of an apportionment that gives Seaside Mall the new employee. (Round your answer to the nearest thousandth.)
Use the apportionment principle to determine which store should receive the new employee.

Summer Hill Galleria
Seaside Mall Galleria    

To determine the relative unfairness, we need to use the concept of *customer-to-sales associate ratios* for each store and assess how the ratios would change with the addition of a new sales associate.

### Step 1: Calculate Current Customer-to-Sales Associate Ratios
1. **Summer Hill Galleria**: 
   \[
   \text{Current Ratio} = \frac{5,589 \text{ customers}}{561 \text{ sales associates}} = 9.965
   \]

2. **Seaside Mall Galleria**: 
   \[
   \text{Current Ratio} = \frac{5,785 \text{ customers}}{675 \text{ sales associates}} = 8.574
   \]

### Step 2: Calculate the Ratios if the New Employee is Added to Each Store
Let's calculate the new customer-to-sales associate ratios when one additional sales associate is added to each store individually.

#### Case 1: Adding One Sales Associate to **Summer Hill Galleria**
- **New Ratio**:
  \[
  \text{New Ratio} = \frac{5,589 \text{ customers}}{561 + 1} = \frac{5,589}{562} \approx 9.947
  \]

#### Case 2: Adding One Sales Associate to **Seaside Mall Galleria**
- **New Ratio**:
  \[
  \text{New Ratio} = \frac{5,785 \text{ customers}}{675 + 1} = \frac{5,785}{676} \approx 8.561
  \]

### Step 3: Determine the Relative Unfairness
The relative unfairness is calculated by comparing the percentage change in customer-to-sales associate ratios after adding the new sales associate to each store.

#### Relative Unfairness if the New Employee is Added to **Summer Hill Galleria**
- Percentage change in customer-to-sales associate ratio:
  \[
  \text{Relative Unfairness} = \left|\frac{9.965 - 9.947}{9.965}\right| \times 100 \approx 0.18\%
  \]

#### Relative Unfairness if the New Employee is Added to **Seaside Mall Galleria**
- Percentage change in customer-to-sales associate ratio:
  \[
  \text{Relative Unfairness} = \left|\frac{8.574 - 8.561}{8.574}\right| \times 100 \approx 0.15\%
  \]

### Step 4: Determine the Best Apportionment
Since **Seaside Mall Galleria** has a lower relative unfairness (0.15%) compared to Summer Hill (0.18%), the best apportionment based on fairness would be to assign the new employee to **Seaside Mall Galleria**.

**Conclusion**: 
The new sales associate should be allocated to **Seaside Mall Galleria** to minimize relative unfairness.

Would you like further explanation on the steps or have any questions? 

---

1. How is relative unfairness calculated for apportionment?
2. Why does a smaller customer-to-sales associate ratio indicate a fairer distribution?
3. What are other methods to decide employee allocation across stores?
4. Could increasing the number of sales associates significantly impact customer satisfaction?
5. Why is rounding important in these calculations?

**Tip:** Always compare relative ratios to gauge distribution fairness in similar apportionment problems.

The table below shows the number of sales associates and the average number of customers per day visiting a store at a company's two department stores. The company is planning to add a new sales associate to one of the stores.
Shopping Mall Location Number of Sales Associates Average Number of Customers Per Day
Summer Hill Galleria 561 5,589
Seaside Mall Galleria 675 5,785
Determine the relative unfairness of an apportionment that gives Summer Hill the new employee. (Round your answer to the nearest thousandth.)

Incorrect: Your answer is incorrect.
Determine the relative unfairness of an apportionment that gives Seaside Mall the new employee. (Round your answer to the nearest thousandth.)
Use the apportionment principle to determine which store should receive the new employee.

Summer Hill Galleria
Seaside Mall Galleria

Explore how to use customer-to-sales associate ratios to determine the optimal apportionment for a new employee across two stores. This problem covers ratio calculations, percentage change, and apportionment principles, ideal for high school students in Grades 10-12.

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