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    Northeast Florida's crushed lime rock shipping requirements

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    Roads for your construction company currently have three construction jobs in Northeast Florida requiring crushed lime rock. Three pits are available to service the company's needs. The sources, destination, tonnage available and cost per tone of shipment are given in the table below.

    Sources Destinations Max tonnage
    cost per ton available
    From to job 1 to job 2 to job 3
    Pit Starke $6 $9 $10 150
    Pit Baldwin $10 $11 $11 175
    Pit Jonesville $4 $5 $12 355
    Job needs 200 100 300 600

    a. Determine the optimal shipping assignment to minimize cost, based on shipping cost alone.

    b. The cost per ton to purchase the rock differs from pit to pit.
    Stark charges $0.67 per ton
    Baldwin $0.65 per ton
    and Jonesville charges $0.80 per ton

    c. Does this change the shipping assignment for minimizing cost? If so, what is
    the new assignment?

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    Solution Preview

    Please see the attached files.

    a) As per the given information the optimal shipping assignment is as follows

    (untitled) Solution
    From To Shipment Cost per unit Shipment cost
    Source 1 Destination 3 150 10 1500
    Source 2 Destination 3 150 11 1650
    Source 2 Dummy 25 0 0
    Source 3 Destination 1 200 4 800
    Source 3 Destination 2 100 5 500
    Source ...

    Solution Summary

    The expert analyzes Northeast Florida's crushed lime risk shipping requirements.