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Two small communities, Alpha and Beta, each have a small landfill. They are considering building a joint landfill to serve both communities (Fig. 3-30). Write an objective function that can be used to minimize the total cost of disposal where the towns would have the option of taking the refuse to their own landfill or to the common facility. They will not be able, however, to take the refuse to each other's landfill. Use the following variables, and state all constraints: a) k.c F = fixed-cost for landfill k ($100,000 per year, regardless of size); subscript c stands for capital c = transportation cost from town i to landfill k ($2/km/ton) W₁ = refuse generated in town i (2000 metric tons per year for Alpha, and 3500 metric tons per year for Beta) Fo operating cost of landfill k ($10/metric ton) = Hints: You'll need to include the transportation distance in the standard objective function, since transportation cost is a function of distance. k,c You'll need to add F to the objective function as an additional term independent of waste tonnage (F only should be multiplied by waste tonnage). k,o b) Solve the objective function for two conditions: (1) when the towns use their own landfills exclusively and ( ; I (2) when only the central shared facility is used by both towns. (

Two small communities, Alpha and Beta, each have a small landfill. They are considering building a joint landfill to serve both communities (Fig. 3-30). Write an objective function that can be used to minimize the total cost of disposal where the towns would have the option of taking the refuse to their own landfill or to the common facility. They will not be able, however, to take the refuse to each other's landfill. Use the following variables, and state all constraints: a) k.c F = fixed-cost for landfill k ($100,000 per year, regardless of size); subscript c stands for capital c = transportation cost from town i to landfill k ($2/km/ton) W₁ = refuse generated in town i (2000 metric tons per year for Alpha, and 3500 metric tons per year for Beta) Fo operating cost of landfill k ($10/metric ton) = Hints: You'll need to include the transportation distance in the standard objective function, since transportation cost is a function of distance. k,c You'll need to add F to the objective function as an additional term independent of waste tonnage (F only should be multiplied by waste tonnage). k,o b) Solve the objective function for two conditions: (1) when the towns use their own landfills exclusively and ( ; I (2) when only the central shared facility is used by both towns. (

Solid Waste Engineering
Solid Waste Engineering
3rd Edition
ISBN:9781305635203
Author:Worrell, William A.
Publisher:Worrell, William A.
Chapter3: Collection
Section: Chapter Questions
Problem 3.12P
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Two small communities, Alpha and Beta, each have a small landfill. They are considering building a joint landfill to serve both communities (Fig. 3-30). a) , Write an objective function that can be used to minimize the total cost of disposal where the towns would have the option of taking the refuse to their own landfill or to the common facility. They will not be able, however, to take the refuse to each other's landfill. Use the following variables, and state all constraints: k.c F = fixed-cost for landfill k ($100,000 per year, regardless of size); subscript c stands for capital c = transportation cost from town i to landfill k ($2/km/ton) W = refuse generated in town i (2000 metric tons per year for Alpha, and 3500 metric tons per year for Beta) F = operating cost of landfill k ($10/metric ton) Hints: You'll need to include the transportation distance in the standard objective function, since transportation cost is a function of distance. You'll need to add Fto the objective function as an additional term independent of waste tonnage (Fonly should be multiplied by waste tonnage). b) Solve the objective function for two conditions: (1) when the towns use their own landfills exclusively and ( G I (2) when only the central shared facility is used by both towns. (..
Transcribed Image Text:Two small communities, Alpha and Beta, each have a small landfill. They are considering building a joint landfill to serve both communities (Fig. 3-30). a) , Write an objective function that can be used to minimize the total cost of disposal where the towns would have the option of taking the refuse to their own landfill or to the common facility. They will not be able, however, to take the refuse to each other's landfill. Use the following variables, and state all constraints: k.c F = fixed-cost for landfill k ($100,000 per year, regardless of size); subscript c stands for capital c = transportation cost from town i to landfill k ($2/km/ton) W = refuse generated in town i (2000 metric tons per year for Alpha, and 3500 metric tons per year for Beta) F = operating cost of landfill k ($10/metric ton) Hints: You'll need to include the transportation distance in the standard objective function, since transportation cost is a function of distance. You'll need to add Fto the objective function as an additional term independent of waste tonnage (Fonly should be multiplied by waste tonnage). b) Solve the objective function for two conditions: (1) when the towns use their own landfills exclusively and ( G I (2) when only the central shared facility is used by both towns. (..
8 km Beta landfill 2 km Proposed joint facility 14 km Figure 3-30 See Problem 3-12. 22 km Beta, Alpha 14 km Alpha landfill 12 11 km
Transcribed Image Text:8 km Beta landfill 2 km Proposed joint facility 14 km Figure 3-30 See Problem 3-12. 22 km Beta, Alpha 14 km Alpha landfill 12 11 km
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