A farm of 300 ha grows maize and soybeans. Yield (ton/ha) depends on fertilizer N (kg/ha) and irrigation water W (mm) as follows:\
• Maize: Y₁ = 0.02√N + 0.001W, 50 ≤ N ≤ 150, 200 ≤ W ≤ 500\
• Soybean: Y₂ = 0.015√N + 0.0012W, 40 ≤ N ≤ 120, 150 ≤ W ≤ 400\
The farm has 30 000 kg of N and 90 000 mm of water available for the whole area (i.e., total N = N·area, total water = W·area). The farmer will apply the same amount of N and the same amount of water to every hectare of each crop (uniform application). Determine the allocation of land (ha of maize and soybeans), the uniform N and W per hectare, and the maximum total production (tonnes).

Question

A farm of 300 ha grows maize and soybeans. Yield (ton/ha) depends on fertilizer N (kg/ha) and irrigation water W (mm) as follows:\
• Maize: Y₁ = 0.02√N + 0.001W,   50 ≤ N ≤ 150, 200 ≤ W ≤ 500\
• Soybean: Y₂ = 0.015√N + 0.0012W,   40 ≤ N ≤ 120, 150 ≤ W ≤ 400\
The farm has 30 000 kg of N and 90 000 mm of water available for the whole area (i.e., total N = N·area, total water = W·area). The farmer will apply the same amount of N and the same amount of water to every hectare of each crop (uniform application). Determine the allocation of land (ha of maize and soybeans), the uniform N and W per hectare, and the maximum total production (tonnes).

Accepted Answer

Apply 100 kg N/ha and 300 mm water/ha; plant 0 ha maize and 300 ha soybeans; maximum production = 153 tonnes

Waec Model Questions Vol1 2022 Geography Question 44

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