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. (
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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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. (..
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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