Question

Annual cost of owning (fixed cost) a particular combine harvester is Rs. 3,00,000 whereas, operating it would cost additional Rs. 6,000 per hectare. If an entrepreneur wishes to offer the machine for custom hiring, the combination of annual use (ha) and custom rate (Rs. ha\(^{-1}\)), respectively, that would fetch him the break-even condition is __________.

• A. 200 and 7,500
• B. 210 and 6,300
• C. 180 and 9,200
• D. 250 and 6,100

Hint:

To find the break-even point for custom hiring, equate the revenue from custom hiring to the total costs, and solve for the custom rate.

Answer 1

The Correct Option is A

Let \( C \) be the annual cost of owning the harvester (Rs. 3,00,000) and \( O \) be the operating cost per hectare (Rs. 6,000). Let \( ha \) represent the annual use in hectares, and \( r \) represent the custom rate in Rs. per hectare. The total annual revenue from custom hiring is given by: \[ \text{Revenue} = r \times ha \] For the entrepreneur to break even, the total revenue must be equal to the total cost, which includes the fixed cost and operating cost. Therefore, the break-even condition is: \[ r \times ha = C + O \times ha \] Substitute the given values: \[ r \times ha = 3,00,000 + 6,000 \times ha \] Now, solve for \( r \): \[ r = 6,000 + \frac{3,00,000}{ha} \] If the entrepreneur wants to break even with 200 hectares of annual use, substitute \( ha = 200 \) into the equation: \[ r = 6,000 + \frac{3,00,000}{200} = 6,000 + 1,500 = 7,500 \] Thus, the break-even condition is satisfied with 200 hectares and a custom rate of Rs. 7,500 per hectare. So, the correct answer is (A) 200 and 7,500.