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The image shows a mathematics problem related to business and economics, focusing on production. Here’s the problem statement and questions translated:

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**Economics and Business Mathematics Problem**

A producer manufactures 28,000 units of goods in the third month, while the total production over six months amounts to 174,000 units.

Determine:
- a) The increase in production each month.
- b) The production amount in the first month.
- c) The production amount in the tenth month.
- d) The total production over one year.

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Let’s assume the monthly production follows an arithmetic sequence, where the production increases by a constant amount each month.

Let:
- \( a_1 \) be the production in the first month,
- \( d \) be the monthly increase in production,
- \( a_n = a_1 + (n-1)d \) be the production in the \(n\)-th month.

### Known dataThe image shows a mathematics problem related to business and economics, focusing on production. Here’s the problem statement and questions translated:

---

**Economics and Business Mathematics Problem**

A producer manufactures 28,000 units of goods in the third month, while the total production over six months amounts to 174,000 units.

Determine:
- a) The increase in production each month.
- b) The production amount in the first month.
- c) The production amount in the tenth month.
- d) The total production over one year.

---

Let’s assume the monthly production follows an arithmetic sequence, where the production increases by a constant amount each month.

Let:
- \( a_1 \) be the production in the first month,
- \( d \) be the monthly increase in production,
- \( a_n = a_1 + (n-1)d \) be the production in the \(n\)-th month.

### Known 
- \( a_3 = 28,000 \) (production in the 3rd month),
- The total production over 6 months: \( S_6 = 174,000 \).

We can solve for the monthly increase (\(d\)) and the first month's production (\(a_1\)) using this information.

I will calculate the answers now.The solution to the problem is as follows:

- The production in the **first month (a₁)** is 24,000 units.
- The monthly increase in production (**d**) is 2,000 units.

Now, let's calculate the other parts:
- The production in the 10th month,
- The total production over 1 year (12 months). I will compute these now.Here are the final answers:

- The production in the **10th month** is 42,000 units.
- The **total production over one year (12 months)** is 420,000 units.

Do you want further details or explanations on any of these steps? 

Here are 5 related questions you might want to explore:
1. How would the solution change if the monthly production followed a geometric sequence?
2. What would the total production be if the monthly increase doubled?
3. How can the production rate be optimized over 12 months to reach a higher total?
4. What is the impact of starting with a lower initial production on total annual output?
5. How could a change in demand affect the production increase over time?

**Tip**: Arithmetic progressions are often used to model gradual increases in production or cost, making it a powerful tool for planning and forecasting in business.

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.

Solve a business mathematics problem where a producer manufactures 28,000 units in the 3rd month, with a total of 174,000 units produced over 6 months. Learn how to calculate the monthly production increase, initial production, production in the 10th month, and total production over a year using arithmetic sequences.

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