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Tree Tops

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

Image showing 3D TreesA manager of a forestry company in Scotland has to decide which trees to plant. There are three main species to choose from, Sitka Spruce, European Larch or Lodgepole Pine.

Whatever trees are planted they have to be thinned after 10 and 20 years and the wood from the thinning is sold for a profit.

Each kind of tree has a different planting cost per hectare, a different growth rate and a different value per hectare depending on the age the tree is felled. All this information is given in the table below.

Planting cost per hectare (thousands of £s) 120 115 130
Profit per hectare from 10 year thin (thousands of £s) 10 15 20
Profit per hectare from 20 year thin (thousands of £s) 40 40 30

Possible income per hectare:

After (years) (thousands of £s) (thousands of £s) (thousands of £s)
30 358 192 123
40 513 469 366
50 693 858 646
60 834 1184 950
70 1127 1158 1144
80 904 1059 1311
90 805 837 1476
100 666 783 1360

What strategy for planting and felling would you recommend to the manager in order to maximise the profit after 70 years, 90 years, more generally?