Assume that you are an engineer with the planning department for a county that contains several major metropolitan areas. The cities are located in a flood plain of a broad, meandering river with mountains overlooking the valley. The cities are under the jurisdiction of a single sewage authority that provides service for the entire area. There are five regional wastewater treatment plants that treat sewage for this metropolitan area. The treatment plants process the waste, and then ship sludge to any of five disposal sites. The disposal sites include two landfills (LF), two land disposal (LD) sites, and one incinerator (INC).
The treatment plants generate the following sludge (lb/day):
WT1 – 2500, WT2 – 6000, WT3 – 4000, WT4 – 6800, WT5 -3000 lb/day
The land fill, disposal sites, and incinerator can accept the following amounts of sludge up to (lb/day):
LF1 – 6700, LF2 – 7300, LD1 – 3000, LD2 – 5000, INCINERATOR – 2000 lb/day
Distances from the wastewater treatment plants to the disposal sites (in miles):
|
LF1 |
LF2 |
LD1 |
LD2 |
INC |
|
|
WT1 |
2 |
6 |
4 |
7 |
9 |
|
WT2 |
6 |
4 |
2 |
3 |
6 |
|
WT3 |
8 |
6 |
3 |
5 |
4 |
|
WT4 |
9 |
7 |
4 |
5 |
3 |
|
WT5 |
8 |
5 |
6 |
3 |
4 |
Transportation Costs (cents per lb per mile):
|
LF1 |
LF2 |
LD1 |
LD2 |
INC |
|
|
WT1 |
20 |
40 |
35 |
15 |
18 |
|
WT2 |
20 |
38 |
34 |
16 |
20 |
|
WT3 |
35 |
17 |
19 |
40 |
22 |
|
WT4 |
18 |
33 |
27 |
17 |
15 |
|
WT5 |
25 |
23 |
20 |
26 |
16 |
Once you get it to the disposal site, the costs for burying, or incineration will be (in cents/lb):
|
at LF1 |
at LF2 |
at LD1 |
at LD2 |
at INC |
|
80 |
73 |
26 |
52 |
105 |
Required: Solve for the minimum sludge disposal costs.