School garden allocation
A school agriculture club has a 200 m² plot, 40 hours of labour per week, and P900 for inputs. It can grow spinach or tomatoes. Spinach: yield 2 kg/m², selling price P15/kg, input cost P5/m², labour 0.1 h/m² per week. Tomatoes: yield 3 kg/m², selling price P12/kg, input cost P9/m², labour 0.3 h/m² per week. The club must supply the school kitchen with at least 120 kg of vegetables and wants to maximise income. A member proposes planting all 200 m² with tomatoes because the yield per square metre is higher.
1. Calculate the income, input cost and labour for the all-tomato plan. Check it against the constraints.
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All 200 m² tomatoes:
- Yield = 200 × 3 = 600 kg.
- Income = 600 × P12 = P7,200.
- Input cost = 200 × P9 = P1,800.
- Labour = 200 × 0.3 = 60 hours per week.
The plan fails two constraints. Input cost P1,800 is double the P900 budget, and 60 hours is above the 40-hour labour limit. It does meet the 120 kg kitchen requirement, but that does not make it feasible. The member looked only at yield per square metre and ignored cost and labour.
2. Find a feasible allocation that meets the 120 kg kitchen requirement and stays within budget and labour. Show calculations.
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One feasible allocation is 180 m² spinach and 0 m² tomatoes.
- Area used = 180 m², within 200 m².
- Input cost = 180 × P5 = P900, exactly the budget.
- Labour = 180 × 0.1 = 18 hours, within 40 hours.
- Yield = 180 × 2 = 360 kg, above the 120 kg kitchen requirement.
- Income = 360 × P15 = P5,400.
A mixed allocation, such as 140 m² spinach and 20 m² tomatoes, also works: cost = P700 + P180 = P880, labour = 14 + 6 = 20 hours, yield = 280 + 60 = 340 kg, income = P4,200 + P720 = P4,920. It is feasible but earns less than the 180 m² spinach plan. The budget is the binding constraint.
3. Evaluate the member’s proposal and recommend a plan, considering at least one non-financial factor.
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The member’s proposal is not practical because it exceeds both the budget and the labour limit. High yield per square metre is not the same as high profit or feasibility.
The 180 m² spinach plan is feasible and gives P5,400 income, but it is risky to grow only one crop. A disease or pest could destroy the whole crop, and the kitchen may prefer variety. A better recommendation may be 140 m² spinach plus 20 m² tomatoes, leaving 40 m² fallow or for a later crop. It still meets the kitchen target, stays within budget and labour, and spreads risk. The club should also check market demand and water supply before planting.