Math Problem Statement

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.

Solution

The 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:

  • a1a_1 be the production in the first month,
  • dd be the monthly increase in production,
  • an=a1+(n1)da_n = a_1 + (n-1)d be the production in the nn-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:

  • a1a_1 be the production in the first month,
  • dd be the monthly increase in production,
  • an=a1+(n1)da_n = a_1 + (n-1)d be the production in the nn-th month.

Known

  • a3=28,000a_3 = 28,000 (production in the 3rd month),
  • The total production over 6 months: S6=174,000S_6 = 174,000.

We can solve for the monthly increase (dd) and the first month's production (a1a_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.

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Math Problem Analysis

Mathematical Concepts

Arithmetic Sequence
Linear Algebra
Production Increase

Formulas

Arithmetic sequence formula: a_n = a_1 + (n-1) * d
Sum of arithmetic sequence: S_n = n/2 * (a_1 + a_n)

Theorems

Arithmetic progression properties

Suitable Grade Level

Grades 10-12 (High School)