# 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

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Excel file contains optimal solution of transportation problems.