Answer:
The yield of the stand if one-tenth of the trees are cut is 360000 board-feet.
Step-by-step explanation:
First, let is find the total amount of fir trees that occupies the area of 24 hectares. (1 hectare = 10000 square meters)
![n = \sigma \cdot A](https://tex.z-dn.net/?f=n%20%3D%20%5Csigma%20%5Ccdot%20A)
Where:
- Surface density, measured in trees per square meter.
- Total area, measured in square meters.
Given that
and
, the total amount of fir trees is:
![n = \left(\frac{1}{20}\,\frac{trees}{m^{2}} \right)\cdot (24\,h)\cdot \left(10000\,\frac{m^{2}}{h} \right)](https://tex.z-dn.net/?f=n%20%3D%20%5Cleft%28%5Cfrac%7B1%7D%7B20%7D%5C%2C%5Cfrac%7Btrees%7D%7Bm%5E%7B2%7D%7D%20%20%5Cright%29%5Ccdot%20%2824%5C%2Ch%29%5Ccdot%20%5Cleft%2810000%5C%2C%5Cfrac%7Bm%5E%7B2%7D%7D%7Bh%7D%20%5Cright%29)
![n = 12000\,trees](https://tex.z-dn.net/?f=n%20%3D%2012000%5C%2Ctrees)
It is known that one-tenth of the tress are cut, whose amount is:
![n_{c} = 0.1 \cdot n](https://tex.z-dn.net/?f=n_%7Bc%7D%20%3D%200.1%20%5Ccdot%20n)
![n_{c} = 0.1 \cdot (12000\,trees)](https://tex.z-dn.net/?f=n_%7Bc%7D%20%3D%200.1%20%5Ccdot%20%2812000%5C%2Ctrees%29)
![n_{c} = 1200\,trees](https://tex.z-dn.net/?f=n_%7Bc%7D%20%3D%201200%5C%2Ctrees)
If each tree will yield 300 board-feet, then the yield related to the trees that are cut is:
![y = S\cdot n_{c}](https://tex.z-dn.net/?f=y%20%3D%20S%5Ccdot%20n_%7Bc%7D)
Where:
- Yield of the tress, measured in board-feet per tree.
- Amount of trees that will be cut, measured in trees.
If
and
, then:
![y = \left(300\,\frac{b-ft}{tree} \right)\cdot (1200\,trees)](https://tex.z-dn.net/?f=y%20%3D%20%5Cleft%28300%5C%2C%5Cfrac%7Bb-ft%7D%7Btree%7D%20%5Cright%29%5Ccdot%20%281200%5C%2Ctrees%29)
![y = 360000\,b-ft](https://tex.z-dn.net/?f=y%20%3D%20360000%5C%2Cb-ft)
The yield of the stand if one-tenth of the trees are cut is 360000 board-feet.