https://r2.erweima.ai/mathbot/image/1726765157412tpn7gmo2.jpg

Let's solve the problem in the image step-by-step.

### Given Data:
- **Number of machines**: 6
- **Batch size**: 100 units per batch
- **Non-production time for each machine**: 12 hours

The table provides the setup time and machining time for each machine:

| Máy | Thời gian chuẩn bị (giờ) | Thời gian gia công (phút) |
|-----|--------------------------|--------------------------|
| 1   | 4                        | 5.0                      |
| 2   | 2                        | 3.5                      |
| 3   | 8                        | 10.0                     |
| 4   | 3                        | 1.9                      |
| 5   | 3                        | 4.1                      |
| 6   | 4                        | 2.5                      |

### (a) Calculate the total production time per batch \((T_{sx} - MLT)\):
1. **Setup Time (Thời gian chuẩn bị)**:
   Total setup time for all machines is the sum of the setup times for each machine.
   \[
   T_{\text{setup}} = 4 + 2 + 8 + 3 + 3 + 4 = 24 \text{ hours}
   \]

2. **Machining Time (Thời gian gia công)**:
   Machining time per unit is given in minutes. Convert to hours:
   - Machine 1: \( \frac{5.0}{60} \times 100 = 8.33 \) hours
   - Machine 2: \( \frac{3.5}{60} \times 100 = 5.83 \) hours
   - Machine 3: \( \frac{10.0}{60} \times 100 = 16.67 \) hours
   - Machine 4: \( \frac{1.9}{60} \times 100 = 3.17 \) hours
   - Machine 5: \( \frac{4.1}{60} \times 100 = 6.83 \) hours
   - Machine 6: \( \frac{2.5}{60} \times 100 = 4.17 \) hours

   Total machining time for 100 units:
   \[
   T_{\text{machining}} = 8.33 + 5.83 + 16.67 + 3.17 + 6.83 + 4.17 = 45 \text{ hours}
   \]

3. **Total Production Time**:
   \[
   T_{\text{sx}} = T_{\text{setup}} + T_{\text{machining}} = 24 + 45 = 69 \text{ hours}
   \]

4. **Manufacturing Lead Time (MLT)**:
   Since it's not explicitly provided, we can assume that it's the total time spent in all operations, so \( MLT = T_{\text{sx}} = 69 \text{ hours} \).

   Therefore, the result for \((T_{sx} - MLT)\) is:
   \[
   (T_{\text{sx}} - MLT) = 0 \text{ hours}
   \]

### (b) Determine the productivity of machine 3:
- **Productivity** is often defined as the output per unit time.
- Machine 3's machining time per unit is \(10.0\) minutes.
- For a batch of 100 units, time taken is \( 16.67 \) hours.
- Productivity = \( \frac{\text{Number of units}}{\text{Time taken}} = \frac{100}{16.67} \approx 6 \) units per hour.

Do you want more details or have any questions?

### Related Questions:
1. How to minimize setup time for this production?
2. What is the impact of increasing batch size on productivity?
3. How to calculate the optimal number of machines required for a given production time?
4. What is the utilization rate of each machine?
5. How to reduce non-production time to increase overall efficiency?

**Tip:** For a detailed time study, always separate setup time and machining time to identify bottlenecks.

Hãy xác định thời gian sản xuất lô hàng (T_{sx} - MLT) và năng suất của máy 3 dựa trên bảng dữ liệu cung cấp.

Learn how to calculate the total production time for a batch of 100 units and determine the productivity of machine 3. This problem uses setup and machining times across multiple machines, involving time conversion and production optimization methods. Suitable for university students studying manufacturing processes.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation