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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

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

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