Linear programming model used in the final paper "Saving the Environment One Tree at a Time: An Application of Quantitative Techniques on the La Mesa Watershed"

1. Given Constants
Carbon Maximum Area
Cost Absorption Trees Covered
Seedling Capacity Hectare Per Tree Biodiversity
X1 Narra Pterocarpus indicus 17.00 72.62 469 0.469 0.15
X2 Mahogany Swietenia macrophylla 15.00 76.28 494 0.494 0.09
X3 Ipil Ipil Leucaena leucocephala 10.00 41.27 304 0.304 -
X4 Gmelina Gmelina arborea 15.00 54.48 688 0.688 0.30
X5 Acacia Acacia auriculiformis 14.00 143.05 391 0.391 0.14
X6 Benguet Pine Pinus roxburghii 12.00 90.61 422 0.422 -
Annual Maintenance Cost is 3% of the seedling cost.

2. Assumptions of the Model
1. Maximum Diameter Class is in the range of 10 -20 dbh
2. Carbon density or absorption capacity is given at 50% of the computed
biomass *
3. Tree choices were limited to fast growing trees with maximum carbon
absorption endemic to the watershed **
4. Full capacity of carbon absorption is assumed at the start of 10 years.
5. Biodiversity mix is based on given standards of the La Mesa Watershed.
* Carbon Budgets Pantabangan - Carranglan Watershed Data - Lasco, Pulhin, Lasco, Roy 2005
** Potential Carbon Sequestration Projects in the Philippines - Lasco, Pulhin, Banaticla 2004

3. Statement of Objectives
If an individual wants to help save the environment via offsetting carbon
emissions by planting trees, how much is needed for this endeavor? And
what is the optimal number of trees per genus that have to be planted to
offset the carbon footprints?
Carbon
Absorption
Capacity
X1 Narra 72.62
X2 Mahogany 76.28 Max Carbon Reduction =
X3 Ipil Ipil 41.27
72.62X1 + 76.28X2 + 41.27X3 + 54.48X4 +
X4 Gmelina 54.48
143.05X5 + 90.61X6
X5 Acacia 143.05
X6 Benguet Pine 90.61

4. Constraints
Total Carbon Reduction Contribution <= Carbon Emmission
Area Covered Total Area Covered <= 284 hectares or 2.272 sqm
Biodiversity Mix Narra <= 15% of the total trees planted
Mahogany <= At least 9% of the total trees planted
Gmelina <= At least 3% of the total trees planted
Acacia <= At least 14% of the total trees planted
Total Ipil Ipil Trees = Total Benguet Pine Trees
Maximum Area Trees Planted per Specie <= Maximum number of trees per hectare

5. Constraints
Total Carbon Reduction Contribution <= Carbon Emmission
Area Covered Total Area Covered <= 284 hectares or 2.272 sqm
Biodiversity Mix Narra <= 15% of the total trees planted
Mahogany <= At least 9% of the total trees planted
Gmelina <= At least 3% of the total trees planted
Acacia <= At least 14% of the total trees planted
Total Ipil Ipil Trees = Total Benguet Pine Trees
Maximum Area Trees Planted per Specie <= Maximum number of trees per hectare
Carbon
Absorption
Capacity
X1 Narra 72.62
X2 Mahogany 76.28 Max Carbon Reduction =
X3 Ipil Ipil 41.27
X4 Gmelina 54.48 72.62X1 + 76.28X2 + 41.27X3 + 54.48X4 +
X5 Acacia 143.05 143.05X5 + 90.61X6
X6 Benguet Pine 90.61

6. Constraints
Total Carbon Reduction Contribution <= Carbon Emmission
Area Covered Total Area Covered <= 284 hectares or 2.272 sqm
Biodiversity Mix Narra <= 15% of the total trees planted
Mahogany <= At least 9% of the total trees planted
Gmelina <= At least 3% of the total trees planted
Acacia <= At least 14% of the total trees planted
Total Ipil Ipil Trees = Total Benguet Pine Trees
Maximum Area Trees Planted per Specie <= Maximum number of trees per hectare
Area
Covered
Per Tree
X1 Narra 0.469
X2 Mahogany 0.494
Total Area Covered =
X3 Ipil Ipil 0.304
.469X1 + .494X2 + .304X3 + .688X4 +
X4 Gmelina 0.688
.391X5 + .422X6
X5 Acacia 0.391
X6 Benguet Pine 0.422

7. Constraints
Total Carbon Reduction Contribution <= Carbon Emmission
Area Covered Total Area Covered <= 284 hectares or 2.272 sqm
Biodiversity Mix Narra <= 15% of the total trees planted
Mahogany <= At least 9% of the total trees planted
Gmelina <= At least 3% of the total trees planted
Acacia <= At least 14% of the total trees planted
Total Ipil Ipil Trees = Total Benguet Pine Trees
Maximum Area Trees Planted per Specie <= Maximum number of trees per hectare
Biodiversity
X1 Narra 0.15
Narra X1 <= .15 (X1 + X2 + X3 + X4 + X5)
X2 Mahogany 0.09
X3 Ipil Ipil - Mahogany X2 <= .09 (X1 + X2 + X3 + X4 + X5)
X4 Gmelina 0.30
Gmelina X4 <= .03 (X1 + X2 + X3 + X4 + X5)
Acacia X5 <= .14 (X1 + X2 + X3 + X4 + X5)
X5 Acacia 0.14
X6 Benguet Pine - Ipil Ipil = B. Pines X2 = X6

8. Constraints
Total Carbon Reduction Contribution <= Carbon Emmission
Area Covered Total Area Covered <= 284 hectares or 2.272 sqm
Biodiversity Mix Narra <= 15% of the total trees planted
Mahogany <= At least 9% of the total trees planted
Gmelina <= At least 3% of the total trees planted
Acacia <= At least 14% of the total trees planted
Total Ipil Ipil Trees = Total Benguet Pine Trees
Maximum Area Trees Planted per Specie <= Maximum number of trees per hectare
Maximum
Tree Per
Hectare
X1 Narra 469 Narra X1 <= 469
X2 Mahogany 494 Mahogany X2 <= 494
X3 Ipil Ipil 304 Ipil Ipil X3 <= 304
X4 Gmelina 688 Gmelina X4 <= 688
X5 Acacia 391 Acacia X5 <= 391
X6 Benguet Pine 422 Benguet Pines X6 <= 422

9. Linear Programming Results
Computed Carbon Emission - 22,000
Total Carbon
Trees Sq M Cost Reduction
Planted Area Covered Breakdown Contribution
Narra 22 10.39 377.30 1,609.54
Mahogany 27 13.10 398.36 2,023.51
Ipil Ipil 59 17.86 587.88 2,424.94
Gmelina 88 60.36 1,316.36 4,779.38
Acacia 41 15.96 571.83 5,838.57
Benguet Pine 59 24.80 705.46 5,324.06
295 142.47 3,957.18 22,000.00