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To solve this problem, we need to calculate the additional labor and overhead cost associated with extending the shift length to meet or exceed the daily demand of 1400 dozen cookies (16,800 cookies). Let's follow the step-by-step approach based on the details provided:

### Step 1: Calculate Current Production Capacity

1. **Current Shift Length**: 7 hours (420 minutes).
2. **Extruder Setup**: 3 cutters working at 25 cookies per minute per cutter.
   
   Therefore, total cookies per minute:
   \[
   3 \text{ cutters} \times 25 \text{ cookies per minute} = 75 \text{ cookies per minute}
   \]

3. **Production per 7-hour shift**:
   \[
   75 \text{ cookies per minute} \times 420 \text{ minutes} = 31,500 \text{ cookies}
   \]

### Step 2: Calculate Batches Completed per Shift

1. **Batch Size**: 8 pounds of dough, standard cookie size is 2 ounces per cookie.
   
   Cookies per batch:
   \[
   8 \text{ pounds} \times 16 \text{ ounces per pound} / 2 \text{ ounces per cookie} = 64 \text{ cookies per batch}
   \]

2. **Number of Batches per 7-hour Shift**:
   \[
   31,500 \text{ cookies} / 64 \text{ cookies per batch} \approx 492.19 \text{ batches}
   \]

### Step 3: Determine Shift Extension

To determine the necessary shift extension, the daily demand must be met or exceeded:

1. **Daily Demand**: 16,800 cookies.
2. **Cookies Produced per Minute**: 75 cookies.
   
   Extra minutes required to meet demand:
   \[
   \frac{16,800 \text{ cookies} - 31,500 \text{ cookies}}{75 \text{ cookies per minute}}
   \]

Since the initial calculation shows that even the current setup exceeds the required demand (16,800 < 31,500), there might be an error in the question.

### Step 4: Calculate Labor and Overhead Increase if Shifts are Extended

1. **Labor and Overhead Cost per Hour**: $230.
2. **Minimum Shift Extension with Break Time**:
   - 7 hours + 45 minutes minimum shift extension = 7.75 hours.
   
   Additional cost:
   \[
   0.75 \text{ hours} \times 230 \text{ dollars per hour} = 172.5 \text{ dollars}
   \]

Given the context, let me know if further elaboration on calculation adjustments is needed.

Would you like to delve deeper into understanding this calculation? Here are some related queries:

1. How does altering break times impact labor costs further?
2. What is the marginal cost per cookie if production is increased beyond current levels?
3. What other efficiencies can be explored without altering shift lengths?
4. How could automation impact labor calculations?
5. What is the breakeven point for further expansion?

**Tip**: Always validate that the demand aligns closely with current production to avoid unnecessary adjustments.

Charlie Cooker wants to analyze the impact of extending shift length to increase the production of C4 Chocolate Chip Crunch Cookies to meet daily demand.

Analyze the impact of extending shift length on the production of C4 Chocolate Chip Crunch Cookies. This detailed problem covers production capacity, labor costs, and batch processing calculations, providing insights into time and resource management in manufacturing.

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