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Figure 1. Initial development of a two-variable graph for the road construction problem, with the miles of rocked roads to be built on the Y-axis, and the amount of woods roads to be built on the X-axis. 10. 8. 6. RR (miles). 4. 2. 0. 0. 2. 4. 6. 8. 10. WR (miles). - PowerPoint PPT Presentation
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RR(miles)
WR(miles)
2 4 6 8 1000
2
4
6
8
10
Figure 1. Initial development of a two-variable graph for the road construction problem, with the miles of rocked roads to be built on the Y-axis, and the amount of woods roads to be built on the X-axis.
RR(miles)
WR(miles)
2 4 6 8 1000
2
4
6
8
10
30,000 WR + 50,000 RR 300,000
Feasible region
Figure 2. The budget constraint for the road construction problem.
RR(miles)
WR(miles)
2 4 6 8 1000
2
4
6
8
10
30,000 WR + 50,000 RR 300,000
RR 1.5
RR 4
WR 2.5 WR 6
Figure 3. A graph of the entire set of constraints to the road construction problem, and the areas related to the constraints where solutions are feasible.
RR(miles)
WR(miles)
2 4 6 8 1000
2
4
6
8
10
RR + WR = 8
RR + WR = 4
Figure 4. Identification of the optimal solution to the road construction problem using a family of objective functions.
RR + WR = 8.4
DS(trees)
CS(trees)
400 800 1,200 1,600 2,00000
400
800
1,200
1,600
2,000
100 DS + 50 CS 80,000
DS 100
CS 250
DS 600
Figure 5. The graphed constraints to the snag development problem, and the identification of the feasible region (gray area).
DS(trees)
CS(trees)
400 800 1,200 1,600 2,00000
400
800
1,200
1,600
2,000
CS + DS = 1,500
Figure 6. The optimal solution to the snag development problem.
Logs(miles)
Boulders(miles)
5 10 15 20 2500
5
10
15
20
25
10,000 Logs + 21,000 Boulders 250,000
Logs 5
Boulders 2.5
Boulders 7.5
Figure 7. The constraints and feasible region (gray area) associated with the fish habitat problem.
Figure 8. Hurricane damage to a pine stand after Hurricane Katrinain 2005.
Figure 9. Identification of the feasible region and optimal solution to the hurricane clean-up problem of cost minimization using a family of objective functions.
200,000
600,000
1,000,000
800,000
400,000
CH 400,000
CPB 300,000
CPB 500,000
CH + CPB 1,000,000
CH ($)
CPB ($)
CH + CPB
0
0 200,000 400,000 600,000 800,000 1,000,000
Logs(miles)
Boulders(miles)
5 10 15 20 2500
5
10
15
20
25
10,000 Logs + 21,000 Boulders 250,000
Logs 5
Boulders 2.5
Boulders 7.5
Boulders + Logs 15
A
B
Figure 10. A modified fish habitat problem, with multiple optimal solutions.
Timbervolume
Wildlifehabitat
A
B
C
D
(Feasible region solutions)
Figure 11. An example of efficient, feasible, inefficient, and infeasible solutions to a broad timber harvest and wildlife habitat management problem.
(Figure for question 7)
Roads
Streams
Streams to be treated with logs or boulders
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