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The image shows a problem in economic and business mathematics, where a producer's production details over six months are given. Here's a breakdown of the problem:

### Problem Summary:
1. **Given:**
   - In the 3rd month, the production was **28,000 units**.
   - The **total production over 6 months** was **174,000 units**.

2. **Questions to solve:**
   - a) **The monthly increase in production**.
   - b) **The production in the first month**.
   - c) **Production in the 10th month**.
   - d) **Total production over 1 year**.

### Let's assume the production follows an arithmetic progression (AP):
- The production in the **nth month** can be represented as:  
  \( P_n = P_1 + (n - 1) \cdot d \)  
  where \( P_n \) is the production in the \(n\)-th month, \( P_1 \) is the first month's production, and \( d \) is the monthly increase in production.

#### Step-by-Step Solution Approach:
1. For month 3, we know:  
   \( P_3 = P_1 + 2d = 28,000 \).
   
2. The total production over 6 months:  
   \( \text{Total}_6 = \frac{6}{2} \cdot (2P_1 + 5d) = 174,000 \).

Now, we can solve these two equations simultaneously to find \( P_1 \) (first month's production) and \( d \) (monthly increase).

Let me calculate this.From the calculations:

- The **production in the first month** (\( P_1 \)) is **24,000 units**.
- The **monthly increase in production** (\( d \)) is **2,000 units**.

### Now let's proceed to answer the remaining questions:

3. **Production in the 10th month**:  
   Using the formula \( P_n = P_1 + (n - 1) \cdot d \), we can find \( P_{10} \).

4. **Total production over 1 year (12 months)**:  
   The total production for 12 months in an arithmetic progression is given by:  
   \[ \text{Total}_\text{12} = \frac{12}{2} \cdot (2P_1 + 11d) \].

I'll calculate these values next.The remaining results are:

- **Production in the 10th month**: **42,000 units**.
- **Total production over 1 year (12 months)**: **420,000 units**.

Would you like further details on the steps involved, or do you have any other questions?

Here are some related questions to expand your understanding:
1. What assumptions are made in using an arithmetic progression for production?
2. How would the results change if production followed a geometric progression instead?
3. How could seasonal variations affect monthly production in real-world scenarios?
4. What are other methods to model production growth over time?
5. How can we calculate total production if the growth rate \(d\) changes mid-year?

**Tip:** Always check if the production pattern fits a linear progression; otherwise, explore other models (like exponential growth).

Seorang produsen menghasilkan barang sebanyak 28.000 unit pada bulan ke-3, sedangkan total produksi selama 6 bulan sebanyak 174.000 unit. Tentukan: a) Kenaikan produksi setiap bulannya b) Besar produksi pada bulan pertama c) Produksi bulan ke-10 d) Total produksi selama 1 tahun

This problem involves a producer's monthly production increase using an arithmetic progression model. Learn how to calculate the monthly increase, first month production, and total production over 1 year, based on given data over 6 months. Ideal for college-level economics or business math students.

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