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?

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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.