A community has two waste sources S1 and S2 having option to dispose waste at either...

A community has two waste sources S1 and S2 having option to dispose waste at either
landfill LF1 at $4/tonne, or LF2 at $6/tonne. S1 and S2 generate waste at 150 tonnes/week and 300
tonnes/week, respectively, and transportation costs are $8/tonne (S1 to LF1), $7/tonne (S1 to LF2),
$6/tonne (S2 to LF1), and $5/tonne (S2 to LF2). (A) (2 points) At which landfills should S1 and S2 dispose
the wastes to minimize total cost of transportation and disposal? (B) (4 points) What are the minimum
costs of transportation and disposal ($/week) for S1, S2, and total community? (C) (4 points) What are
the minimum transportation costs ($/week) for S1, S2, and total community?

Solutions

Expert Solution

Waste at source S1 = 150 tonnes/week and at S2 = 300 tonnes /week

Disposal cost at LF1 = $4/ tonne and disposal cost at LF2 = $6/tonne

Transportation cost from S1 to LF1 = $8/tonne and S1 to LF2 = $7/tonne .

Thus total disposal and transportation cost for waste from S1 to :

LF1 = $12 /tonne

LF2 = $13/tonne . Thus waste from S1 should be disposed at LF1 for minimizing cost of transportation and disposal.

Similarly for S2 , transportation cost to LF1 = $6/tonne and to LF2 = $5/tonne . Thus total cost of transportation and disposal from S2 to :

LF1 = $10/tonne

LF2 = $11/tonne . Thus waste from S2 should be disposed at LF1 to minimise cost of transportation and disposal.

Minimum cost of transportation and disposal for : S1 = $12*150 = $1800 per week

S2 = $10*300 = $3000 per week

Total Community = $(1800+3000) = $4800 per week

Minimum cost of transportation for :

S1 = $7*150 = $1050 per week

S2 = $5*300 = $1500 per week

Total Community = $(1050+1500) = $2550 per week

Ally Wells answered 6 months ago

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