Subtopic: Cost analysis of implements and tractors
Question Statement:
A 4.2 m self-propelled combine harvester operating at a forward speed of 3.5 km·h⁻¹ is used to harvest wheat in an area of 300 ha in a year at a field efficiency of 75 %. Consider the variable cost to be linearly related to the actual hours of operation. To bring down the cost of operation per hour by 15 %, the change in area required to be harvested per year, in ha, is __________. (Rounded off to 2 decimal places)
Options:
(A) 52.94
(B) 53.74
(C) 55.80
(D) 57.65
Official Answer Key:
A
Step-by-Step Solution & Explanation
Step 1 — cost structure. Annual cost = fixed cost (independent of use) + variable cost (linear in hours). The cost of operation per hour is therefore dominated by the spreading of the fixed cost over the annual hours of use:
Cost per hour ∝ 1/(annual hours of use)
Step 2 — effective field capacity is constant (width, speed and field efficiency are unchanged):
EFC = (W × S × η)/10 = (4.2 × 3.5 × 0.75)/10 = 1.1025 ha·h⁻¹
Since hours = area/EFC and EFC is fixed, annual hours ∝ annual area. Hence:
Cost per hour ∝ 1/(annual area)
Step 3 — required area for a 15% cost reduction:
New cost = 0.85 × old cost ⇒ new area = old area/0.85
A₂ = 300/0.85 = 352.94 ha
Step 4 — change in area:
ΔA = 352.94 − 300 = 52.94 ha
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