Question

The cost of operation of an implement in an area of Y hectare is given by 20 + 15Y, while the revenue from the area is given by 200 + 5Y. What will be the total area of operation by the machine to achieve break even?

• A. 9 ha
• B. 10 ha
• C. 15 ha
• D. 18 ha

Hint:

To find the break-even point quickly, subtract the variable rates to find the net rate ($15 - 5 = 10$) and divide the difference in fixed values ($200 - 20 = 180$) by this net rate:
\[ Y = \frac{180}{10} = 18\text{ ha} \]

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
The break-even point is a financial milestone where the total cost associated with an activity or operation equals the total revenue generated from it.
At this point, there is neither profit nor loss.
This analysis is used to determine the minimum scale of operation required for a farm implement to be economically viable.
Key Formula or Approach:
Let:
- \( C \) be the total cost of operation.
- \( R \) be the total revenue generated.
- \( Y \) be the area of operation in hectares.
At the break-even point:
\[ C = R \]

Step 2: Detailed Explanation:
Let us calculate the break-even area step-by-step:
1. Write down the given mathematical expressions for cost and revenue:
- Cost equation:
\[ C = 20 + 15Y \]
- Revenue equation:
\[ R = 200 + 5Y \]
2. Set the cost equal to the revenue to find the break-even condition:
\[ 20 + 15Y = 200 + 5Y \]
3. Group the terms containing \( Y \) on the left side of the equation, and the constant terms on the right side:
\[ 15Y - 5Y = 200 - 20 \]
4. Simplify both sides:
\[ 10Y = 180 \]
5. Solve for \( Y \):
\[ Y = \frac{180}{10} = 18 \]
Therefore, the machine must operate over an area of \( 18 \text{ hectares} \) to break even.

Step 3: Final Answer:
The total area of operation to achieve break-even is 18 ha.