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    Quantitative Methods

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    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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    https://brainmass.com/statistics/quantative-analysis-of-data/quantitative-methods-121068

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    Solution Summary

    Excel file contains optimal solution of transportation problems.

    $2.19

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