To solve this problem, we need to find the maximum amount of money we can earn per round of harvest.
We need to find the average income per year so we know what year to cut them and which trees to plant
Sitka Spruce: SS, -120k
European Larch: EL -115k
Lodgepole Pine: LP -130k
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: -80
Now we need to actually cut down the trees.
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, 14.76, 12.46, 12.73, 15.1, (no point calculating past this point as the value drops while years increase)
EL: 4.4, 10.23, 15.76, 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 50 years.
The question says to calculate th 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 15760£ a year and 1576000£ after 100 years.