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The problem asks to calculate the total revenue and gross profit for a manufacturer producing three products \(A\), \(B\), and \(C\), which are sold in two markets.

### Given:
- Sales volumes in two markets:
\[
\text{Market 1: } \begin{bmatrix} 10000 & 2000 & 18000 \end{bmatrix}
\]
\[
\text{Market 2: } \begin{bmatrix} 6000 & 20000 & 8000 \end{bmatrix}
\]
Where each column represents the quantity sold for product \(A\), \(B\), and \(C\) respectively.

- Unit sale prices:
  - \(A\): Tk. 8000
  - \(B\): Tk. 9000
  - \(C\): Tk. 7000

- Unit costs:
  - \(A\): Tk. 4000
  - \(B\): Tk. 4500
  - \(C\): Tk. 3000

### Steps to solve:
1. **Revenue Calculation:**
   - Total revenue for each market can be calculated as:
   \[
   \text{Revenue} = (\text{quantity of A} \times \text{price of A}) + (\text{quantity of B} \times \text{price of B}) + (\text{quantity of C} \times \text{price of C})
   \]

2. **Cost Calculation:**
   - Total cost for each market can be calculated using the same method but with unit costs instead of prices.
   
3. **Gross Profit Calculation:**
   - Gross profit = Total revenue - Total cost.

Let's perform these calculations.### Results:
1. **Total Revenue:** Tk. 508,000,000
2. **Total Cost:** Tk. 241,000,000
3. **Gross Profit:** Tk. 267,000,000

These values were obtained using matrix algebra, calculating both revenue and costs based on the sales volumes in two markets, the unit prices, and the unit costs for products \(A\), \(B\), and \(C\).

Would you like further details or explanations on any part of the process?

### Related Questions:
1. How do we represent such calculations using matrices?
2. What is the significance of gross profit for a business?
3. How can this type of analysis help in decision-making for production?
4. How would changes in unit prices affect the revenue and profit?
5. What role does cost control play in increasing gross profit?

### Tip:
Always verify unit costs and selling prices for accurate revenue and profit calculations.

A television manufacturer produces three products A, B, and C, which are sold in two markets. The annual sales volumes for each product in both markets are given, along with unit sale prices and unit costs. The task is to calculate the total revenue and gross profit using matrix algebra.

Learn how to calculate the total revenue and gross profit for a television manufacturer selling three products across two markets using matrix algebra. Explore detailed calculations involving unit prices, costs, and sales volumes.

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