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Quantitative Methods

Three quarries produce lime which is then shipped to five warehouses

Quarry Tons Lime
1 200
2 100
3 150

Transport Costs (per ton)
Quarry 1 2 3 4 5
1 $5 $1 $6 $3 $1
2 $2 $3 $4 $5 $4
3 $4 $2 $3 $2 $3
Demand 80 90 100 70 60
(tons)

Minimize the transportation costs

Answer:
Quarry Tones of lime
1 200
2 100
3 150
450
Transportation costs(per ton)
Quarry 1 2 3 4 5
1 $5.00 $1.00 $6.00 $3.00 $1.00
2 $2.00 $3.00 $4.00 $5.00 $4.00
3 $4.00 $2.00 $3.00 $2.00 $3.00
Demand 80 90 100 70 60 400

As demand(400) is less than supply(450), this is an unbalanced problem. The supply constraints would have <= sign.

Transportation costs(per ton)
Warehouse
Quarry 1 2 3 4 5
1 $5.00 $1.00 $6.00 $3.00 $1.00
2 $2.00 $3.00 $4.00 $5.00 $4.00
3 $4.00 $2.00 $3.00 $2.00 $3.00

Tons of lime shipped
Warehouse
Quarry 1 2 3 4 5 Shipped Capacity
1 0 90 0 20 60 170 <= 200
2 80 0 0 0 0 80 <= 100
3 0 0 100 50 0 150 <= 150
80 90 100 70 60
= = = = =
Demand 80 90 100 70 60

Total transportation cost $770.00

ANSWER:
Ship 90 tons from Quarry 1 to warehouse 2, 20 tons from Quarry 1 to warehouse 4, 60 tons from quarry 1 to warehouse 5
80 tons from Quarry 2 to warehouse 1, 100 tons from quarry 3 to warehouse 3, and 50 tons from quarry 3 to warehouse 4
at total transportation cost of $770.

this is a standard transportation problem - please solve

Solution Preview

Please see attachments for complete details and explanations. The optimal solution in excel file is ...

Solution Summary

Excel file contains optimal solution of transportation problems.

$2.19