1. Create a spreadsheet model for this problem.

2. What is the optimal solution?

3. Suppose the cost of building the road connecting areas 4 and 5 dropped to $12,000. What impact does this have on the optimal solution?

The state of Virginia is one of the largest producers of wood furniture in the United States, with the furniture industry accounting for 50% of value added to wood materials. Over the past 40 years, the inventory volume of wood in Virginia's forests has increased by 81%. Today, 15.4 million acres, which is well over half of the state, are covered in forest. Private owners hold 77% of this land. When making decisions about which trees to harvest, forestry professionals consider many factors and must follow numerous laws and regulations.

Figure 6.36 depicts a tract of forested land that has been sectioned off into 12 harvestable areas, indicated by dashed lines. Area 2 provides the only access to the forest via a paved road, so any timber cut must ultimately be transported out of the forest through area 2. Currently, there are no roads through this forest, so to harvest the timber, forest roads will need to be built. The allowable routes for these roads are also shown in Figure 6.36 and are determined largely based on the geography of the land and location of streams and wildlife habitats.

FIGURE 6.36

Not all areas of the forest have to be harvested. However, to harvest any area, a forest road must be built to that area. The cost of building each section of forest road (in $1000s) is indicated in the figure. Finally, the net value of the harvestable timber in each area is estimated as follows:

Which areas should be harvested and what roads should be built to make the most profitable use of this forest?

Transcribed Image Text:

10 $9 $15 $14 S11 S0 $15 $13 $12 1, $121 112 $12 $13 $10 Harvested Value (in $1000s) Area 2 3 7 10 11 12 Value $15 $7 $10 $12 $8 $17 $14 $18 $13 $12 $10 $11