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Satellite TV manufacturing businesses tend to have what economists call "economies of scale." When economies of scale exist, bigness can be its own reward. The more TV's you manufacture in a single run, lower the costs per unit, which in turn increases your bottom-line margins.
Keeping that in mind, a T.V. manufacturing company increases its production uniformly by fixed number every year. The company produces 8000, sets in the `6^(th)` year and 11,300 sets in the `9^(th)` year.
The company's production of the first year is:

A

2000

B

2500

C

3000

D

5000

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem, we need to determine the production of the first year based on the information given about the production in the 6th and 9th years. ### Step-by-Step Solution: 1. **Define the Variables**: Let the production in the first year be \( x \) and the fixed increase in production each year be \( d \). 2. **Establish the Production Equations**: - In the 6th year, the production can be expressed as: \[ \text{Production in 6th year} = x + 5d = 8000 \] - In the 9th year, the production can be expressed as: \[ \text{Production in 9th year} = x + 8d = 11300 \] 3. **Set Up the System of Equations**: We now have two equations: \[ (1) \quad x + 5d = 8000 \] \[ (2) \quad x + 8d = 11300 \] 4. **Subtract the First Equation from the Second**: To eliminate \( x \), we subtract equation (1) from equation (2): \[ (x + 8d) - (x + 5d) = 11300 - 8000 \] This simplifies to: \[ 3d = 3300 \] 5. **Solve for \( d \)**: Divide both sides by 3: \[ d = \frac{3300}{3} = 1100 \] 6. **Substitute \( d \) Back into One of the Equations**: Now substitute \( d = 1100 \) back into equation (1): \[ x + 5(1100) = 8000 \] Simplifying this gives: \[ x + 5500 = 8000 \] 7. **Solve for \( x \)**: Subtract 5500 from both sides: \[ x = 8000 - 5500 = 2500 \] ### Conclusion: The production of the first year is \( \boxed{2500} \).
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Knowledge Check

  • Satellite TV manufacturing businesses tend to have what economists call "economies of scale." When economies of scale exist, bigness can be its own reward. The more TV's you manufacture in a single run, lower the costs per unit, which in turn increases your bottom-line margins. Keeping that in mind, a T.V. manufacturing company increases its production uniformly by fixed number every year. The company produces 8000, sets in the 6^(th) year and 11,300 sets in the 9^(th) year. The company's production of the 8th year is:

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    D
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  • Satellite TV manufacturing businesses tend to have what economists call "economies of scale." When economies of scale exist, bigness can be its own reward. The more TV's you manufacture in a single run, lower the costs per unit, which in turn increases your bottom-line margins. Keeping that in mind, a T.V. manufacturing company increases its production uniformly by fixed number every year. The company produces 8000, sets in the 6^(th) year and 11,300 sets in the 9^(th) year. The company's total production of the first 6 years is:

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  • Satellite TV manufacturing businesses tend to have what economists call "economies of scale." When economies of scale exist, bigness can be its own reward. The more TV's you manufacture in a single run, lower the costs per unit, which in turn increases your bottom-line margins. Keeping that in mind, a T.V. manufacturing company increases its production uniformly by fixed number every year. The company produces 8000, sets in the 6^(th) year and 11,300 sets in the 9^(th) year. The company's production increases every year by:

    A
    2500
    B
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    C
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    D
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