Nursery economics and bed geometry before the planting season
A central nursery in the Satpura foothills raised 27,000 seedlings of three species last season. The figures are: Sal (Shorea robusta) - 12,000 raised, cost Rs 48,000, surviving after six months 8,400; Arjun (Terminalia arjuna) - 9,000 raised, cost Rs 27,000, surviving 7,200; Bamboo (Dendrocalamus strictus) - 6,000 raised, cost Rs 30,000, surviving 5,400. The Range Officer has an additional Rs 20,000 and must decide which species to expand. Separately, the main bed is rectangular, 40 m by 25 m. Two cross paths, each 2 m wide, run across the full 25 m width; one 3 m wide path runs along the full 40 m length on the northern boundary. Planting is to be done at 25 cm by 25 cm spacing. A field assistant states: 'The average survival of this nursery is 80 per cent, so to plant the whole bed we need to raise only 12,480 seedlings.'
1. Calculate survival percentage and cost per surviving seedling for each species, rank them, and recommend how the additional Rs 20,000 should be spent.
Read the worked answer
Work per surviving seedling, not per seedling raised.
Sal: 8,400 ÷ 12,000 = 70.0 per cent; Rs 48,000 ÷ 8,400 = Rs 5.71 per survivor. Arjun: 7,200 ÷ 9,000 = 80.0 per cent; Rs 27,000 ÷ 7,200 = Rs 3.75 per survivor. Bamboo: 5,400 ÷ 6,000 = 90.0 per cent; Rs 30,000 ÷ 5,400 = Rs 5.56 per survivor.
Ranking from cheapest to dearest: Arjun, Bamboo, Sal.
Use of Rs 20,000. Cost of raising one seedling: Sal Rs 4, Arjun Rs 3, Bamboo Rs 5. Assuming the same rates and survival, the extra money yields: Sal 5,000 raised × 0.70 = 3,500 survivors; Arjun 6,667 raised × 0.80 = 5,333 survivors; Bamboo 4,000 raised × 0.90 = 3,600 survivors. Arjun gives the most survivors for the money.
Caveat that earns the marks. This is a cost calculation, not a silvicultural one. Before spending, check whether the plantation site suits Arjun, whether seed or root-trainer stock is available, whether the marginal cost is really Rs 3 per seedling at higher volume, and what happens after out-planting - a cheap seedling that dies in the field is the costliest of all.
2. Find the plantable area of the bed and the number of planting points. How many seedlings must actually be raised to fill the bed?
Read the worked answer
Area first, then density.
Total bed area = 40 m × 25 m = 1,000 sq m. Cross paths: 2 paths × 2 m × 25 m = 100 sq m. Length path: 3 m × 40 m = 120 sq m, taken along the boundary so it does not overlap the cross paths. Total path area = 100 + 120 = 220 sq m. Plantable area = 1,000 − 220 = 780 sq m.
Spacing 25 cm × 25 cm = 0.25 m × 0.25 m = 0.0625 sq m per planting point. Planting points = 780 ÷ 0.0625 = 12,480.
Seedlings to raise. If 80 per cent of what is raised survives to planting size, raising 12,480 gives only 12,480 × 0.80 = 9,984 plantable seedlings, leaving 2,496 gaps. The requirement is 12,480 ÷ 0.80 = 15,600 seedlings raised. A further margin of 5–10 per cent is usual for culling, transport damage and casualties, taking the figure to roughly 16,400–17,200. Note that this also explains the field assistant's error: 12,480 is the number of planting points, not the number to raise.
3. Evaluate the field assistant's claim of 80 per cent average survival, and state what further data you would demand before approving expansion.
Read the worked answer
The 80 per cent is the wrong kind of average.
Adding 70, 80 and 90 and dividing by three gives 80 per cent - but that treats a batch of 12,000 as equal to a batch of 6,000. The nursery-level figure must be weighted by numbers raised: total survivors = 8,400 + 7,200 + 5,400 = 21,000 out of 27,000 raised, which is 77.8 per cent. The unweighted mean overstates performance by about 2.2 percentage points, and the overstatement would grow if the cheapest species in numbers were also the worst performer. This is the standard trap of averaging percentages instead of pooling counts.
The second error is treating planting points as seedlings to be raised. With 12,480 points and a true 77.8 per cent survival, the requirement is 12,480 ÷ 0.778 = about 16,041 seedlings, not 12,480 - a shortfall of over 3,500.
Before approving expansion, demand: out-planting survival for each species at the actual site; soil and rainfall suitability of the proposed plantation area; germination percentage and seed/root-stock availability; culling and transport wastage rates; whether marginal cost per seedling holds at higher volume; and the species mix the working plan actually requires. Cost per survivor alone must not decide the species.