During a 5‑hour harvest the farm must run a combine harvester (150 kW) and a tractor (80 kW) simultaneously. They are powered by a diesel generator rated at 250 kW that consumes 0.25 L kWh⁻¹ at full load and operates at 85 % efficiency. Diesel costs ₦550 per litre.

(a) Assuming the generator runs at the combined load, calculate the minimum fuel required and the total fuel cost for the 5 h operation.
(b) If instead two smaller generators each rated at 150 kW are used, each consuming 0.28 L kWh⁻¹, compare the total fuel cost with that of the single generator and state which option is more economical.

Question

During a 5‑hour harvest the farm must run a combine harvester (150 kW) and a tractor (80 kW) simultaneously. They are powered by a diesel generator rated at 250 kW that consumes 0.25 L kWh⁻¹ at full load and operates at 85 % efficiency. Diesel costs ₦550 per litre.

(a) Assuming the generator runs at the combined load, calculate the minimum fuel required and the total fuel cost for the 5 h operation. 
(b) If instead two smaller generators each rated at 150 kW are used, each consuming 0.28 L kWh⁻¹, compare the total fuel cost with that of the single generator and state which option is more economical.

Accepted Answer

(a) Fuel needed = 287.5 L; cost = ₦158,125. (b) Two smaller generators would use 322 L costing ₦177,100, so the single 250 kW generator is more economical.

Neco 2021 Agricultural Science Question 50

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