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# Tree Tops

In the first place European Larch is the cheapest tree to build when you start your farming because it cost the lowest.

After 10 years and 20 years, we need to thin the trees.

Rates:

SS: +50k

EL: +55k

LP: +50k

The total cost for planting and thinning is:

SS: -70k

EL: -60k

LP: -80k

After 30 years, the Sitka Spruce will make the most profit

After 40 years, the Sitka Spruce will make the most profit

After 50 years, the European Larch will make the most profit

After 60 and 70 years, the European Larch will make the most profit.

After 80, 90, 100 years, the European Larch and the Sitka Spruce lost value, the Lodgepole Pine will make the most profit.

Best in 0,10,20,50,60,70: European Larch

Best in 30,40: Sitka Spruce

Best in over 80: Lodgepole Pine

I saw that if you keep a pine tree for 90 years you get £1,476,000 which was the largest amount. Then you'd add [ £50,000] (money gained from thinning at 10 and 20 years) then you'd take away £130,000 (cost of planting) giving you [ £1,396,000] per hectare.

For the [other trees], using the above method you would select the highest amount then and [add the thinning price], then take away the [planting] price.

Ziniu found the profit per year to find a better strategy:

To find the optimal rates, we need to divide the amount of money gained by the years it takes to grow the trees to that stage so we can find the most efficient time/tree type to maximise profits. We need to also factor in the cost of planting and the gains of thinning as that may affect our results.

Calculation:

(amount gained from cutting + money gained from thinning - planting costs) divided by years it took to plant to that stage

Amount shown is in thousands of £

Tree name, after 30 years, after 40 years, etc

SS: 9.6, 11.1, 12.46, 12.73, 15.1, (no point calculating past this point as the value drops while years increase)

EL: 4.4, 10.23, 15.96, 18.73, 15.68, (no point calculating past this point as the value drops while years increase)

LP: 1.43, 7,15, 11,32, 14.5, 15.2, 15.39, 15.51 (no point calculating past this point as the value drops while years increase)

The most time and money efficient planting method is European Larch 60 years.

The question says to calculate the maximum amount of money earned in 100 years. 50, 20 and 10 are all multiples of 100. Planting and cutting trees at that time would maximise the efficiency of the plantation.

The most efficient plantation method would be EL 50 years, gaining 15960 £

a year and 1596000 £ after 100 years.

As well as replanting after chopping down the forest, Edward came up with a clever and detailed strategy involving planting different kinds of trees at the same time. Click here to watch Edward's video. Note that Edward has interpreted the thinning process in a different way.

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Age 14 to 16

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- Problem
- Getting Started
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- Which tree should you choose to minimise the cost of planting the forest?

In the first place European Larch is the cheapest tree to build when you start your farming because it cost the lowest.

- Which tree should you choose to minimise your loss after 20 years?

After 10 years and 20 years, we need to thin the trees.

Rates:

SS: +50k

EL: +55k

LP: +50k

The total cost for planting and thinning is:

SS: -70k

EL: -60k

LP: -80k

- What would the profit be for each type of tree after 30, 40, and 50 years?

After 30 years, the Sitka Spruce will make the most profit

After 40 years, the Sitka Spruce will make the most profit

After 50 years, the European Larch will make the most profit

After 60 and 70 years, the European Larch will make the most profit.

After 80, 90, 100 years, the European Larch and the Sitka Spruce lost value, the Lodgepole Pine will make the most profit.

Best in 0,10,20,50,60,70: European Larch

Best in 30,40: Sitka Spruce

Best in over 80: Lodgepole Pine

- What's the maximum profit you could make after 100 years?

I saw that if you keep a pine tree for 90 years you get £1,476,000 which was the largest amount. Then you'd add [ £50,000] (money gained from thinning at 10 and 20 years) then you'd take away £130,000 (cost of planting) giving you [ £1,396,000] per hectare.

For the [other trees], using the above method you would select the highest amount then and [add the thinning price], then take away the [planting] price.

Ziniu found the profit per year to find a better strategy:

To find the optimal rates, we need to divide the amount of money gained by the years it takes to grow the trees to that stage so we can find the most efficient time/tree type to maximise profits. We need to also factor in the cost of planting and the gains of thinning as that may affect our results.

Calculation:

(amount gained from cutting + money gained from thinning - planting costs) divided by years it took to plant to that stage

Amount shown is in thousands of £

Tree name, after 30 years, after 40 years, etc

SS: 9.6, 11.1, 12.46, 12.73, 15.1, (no point calculating past this point as the value drops while years increase)

EL: 4.4, 10.23, 15.96, 18.73, 15.68, (no point calculating past this point as the value drops while years increase)

LP: 1.43, 7,15, 11,32, 14.5, 15.2, 15.39, 15.51 (no point calculating past this point as the value drops while years increase)

The most time and money efficient planting method is European Larch 60 years.

The question says to calculate the maximum amount of money earned in 100 years. 50, 20 and 10 are all multiples of 100. Planting and cutting trees at that time would maximise the efficiency of the plantation.

The most efficient plantation method would be EL 50 years, gaining 15960 £

a year and 1596000 £ after 100 years.

As well as replanting after chopping down the forest, Edward came up with a clever and detailed strategy involving planting different kinds of trees at the same time. Click here to watch Edward's video. Note that Edward has interpreted the thinning process in a different way.

Euler found four whole numbers such that the sum of any two of the numbers is a perfect square...

The diagram illustrates the formula: 1 + 3 + 5 + ... + (2n - 1) = nÂ² Use the diagram to show that any odd number is the difference of two squares.