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Part 1
A boat manufacturer has 152 new boats of a new model to be apportioned to four dealerships. The manufacturer decides to apportion the boats based on the number of boats each dealership sold in the previous year. The number of boats sold by each dealership is shown below. Use the table to answer parts a through c.
Dealership
A
B
C
D
Total
 
Annual Sales
5126
4124
3352
2294
14 comma 896
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Part 1
​a) Determine the standard divisor.
  
98
​(Type an integer or decimal rounded to the nearest hundredth as​ needed.)
Part 2
​b) Determine each​ dealership's standard quota.
Dealership
A
B
C
D
Total
Annual sales
5126
4124
3352
2294
14 comma 896
Standard quota
  
enter your response here
  
enter your response here
  
enter your response here
  
enter your response here
​(Type integers or decimals rounded to the nearest hundredth as​ needed.)

To solve this, let's go through each part step-by-step.

### Part (a): Determine the Standard Divisor
The standard divisor is calculated by dividing the total number of boats available by the total sales of all dealerships. 

Given:
- Total boats available = 152
- Total annual sales = 14,896

The formula for the standard divisor \( S \) is:
\[
S = \frac{\text{Total boats available}}{\text{Total annual sales}}
\]

Substitute the values:
\[
S = \frac{152}{14896} \approx 0.0102
\]

Thus, the standard divisor is approximately **0.0102**.

---

### Part (b): Determine Each Dealership’s Standard Quota
The standard quota for each dealership is calculated by multiplying each dealership’s annual sales by the standard divisor.

The formula for each dealership’s standard quota \( Q_i \) is:
\[
Q_i = \text{Annual Sales of Dealership} \times S
\]

Let's calculate each dealership's standard quota using \( S \approx 0.0102 \).

#### Dealership A:
\[
Q_A = 5126 \times 0.0102 \approx 52.89
\]

#### Dealership B:
\[
Q_B = 4124 \times 0.0102 \approx 42.67
\]

#### Dealership C:
\[
Q_C = 3352 \times 0.0102 \approx 34.99
\]

#### Dealership D:
\[
Q_D = 2294 \times 0.0102 \approx 23.40
\]

---

### Summary of Results:
- **Standard Divisor**: \( 0.0102 \)
- **Standard Quotas** (rounded to the nearest hundredth):
  - Dealership A: **52.89**
  - Dealership B: **42.67**
  - Dealership C: **34.99**
  - Dealership D: **23.40**

Would you like a further breakdown of these calculations or additional explanations?

---

### Related Questions:
1. How would the standard quotas change if the total number of boats available increased?
2. What would happen to each dealership’s quota if the annual sales were adjusted for inflation?
3. How can rounding rules affect the final number of boats each dealership receives?
4. How would we approach apportioning a limited resource if the total sales were unknown?
5. Can you explain why the standard divisor is an average unit allocation and how it helps in proportional distribution?

### Tip:
When solving apportionment problems, always check that your total allocations closely match the original total to ensure a fair distribution.

A boat manufacturer has 152 new boats of a new model to be apportioned to four dealerships. The manufacturer decides to apportion the boats based on the number of boats each dealership sold in the previous year. The number of boats sold by each dealership is shown below.

Dealership
A
B
C
D
Total

Annual Sales
5126
4124
3352
2294
14,896

Part (a): Determine the standard divisor. (Type an integer or decimal rounded to the nearest hundredth as needed.)

Part (b): Determine each dealership's standard quota. (Type integers or decimals rounded to the nearest hundredth as needed.)

Learn how to determine the standard divisor and calculate each dealership's quota in a boat apportionment problem. Given sales data and a total boat supply, calculate fair allocations for dealerships A, B, C, and D based on their previous sales. This problem covers proportional allocation, relevant formulas, and apportionment theory, suitable for Grades 9-12.

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