A large company has four divisions with 

250250​, 

310310​, 

390390​, 

and 

410410 

​employees, respectively. A total of 

2929 

computer technicians must be allocated to the four divisions according to their size. Find the standard quota for each division. 

Question content area bottom

Part 1

The standard quota for the division with 

250250 

employees is 

enter your response here​, 

the standard quota for the division with 

310310 

employees is 

enter your response here​, 

the standard quota for the division with 

390390 

employees is 

enter your response here​, 

and the standard quota for the division with 

410410 

employees is 

enter your response here.

​(Round to the nearest hundredth as​ needed.)

To find the standard quota for each division, you need to allocate the 29 computer technicians in proportion to the number of employees in each division. The standard quota for each division can be calculated using the formula:

\[
\text{Standard Quota} = \left(\frac{\text{Number of Employees in the Division}}{\text{Total Number of Employees}}\right) \times \text{Total Number of Technicians}
\]

### Step 1: Calculate the total number of employees.
\[
250 + 310 + 390 + 410 = 1360
\]

### Step 2: Calculate the standard quota for each division.

1. **For the division with 250 employees**:
   \[
   \text{Standard Quota} = \left(\frac{250}{1360}\right) \times 29 \approx 5.33
   \]

2. **For the division with 310 employees**:
   \[
   \text{Standard Quota} = \left(\frac{310}{1360}\right) \times 29 \approx 6.61
   \]

3. **For the division with 390 employees**:
   \[
   \text{Standard Quota} = \left(\frac{390}{1360}\right) \times 29 \approx 8.31
   \]

4. **For the division with 410 employees**:
   \[
   \text{Standard Quota} = \left(\frac{410}{1360}\right) \times 29 \approx 8.74
   \]

### Final Standard Quotas:

- **For the division with 250 employees**: approximately **5.33**
- **For the division with 310 employees**: approximately **6.61**
- **For the division with 390 employees**: approximately **8.31**
- **For the division with 410 employees**: approximately **8.74**

If you have any further questions or need additional details, feel free to ask!

---

**Relative Questions:**

1. How would the standard quotas change if there were 40 technicians instead of 29?
2. What is the significance of rounding to the nearest hundredth in this context?
3. How could you allocate technicians if the standard quota resulted in decimal values?
4. What if one division had twice as many employees as another—how would that affect the quota?
5. Could this method be applied to allocating other resources, like budgets or office space?

**Tip:** Always ensure that the total of the allocated resources (in this case, technicians) equals the original total after allocation.

Learn how to calculate the standard quota for divisions based on the number of employees and total technicians allocated. Detailed step-by-step solution provided for divisions with 250, 310, 390, and 410 employees, rounding to the nearest hundredth as needed.

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