How to Minimize Shipping Costs for Oil Supply Distribution

How should the oil be supplied to minimize shipping costs?

Outlet S1 should send ?? barrels to distributor D1.

Answer:

To minimize shipping costs, we can use the transportation method known as the Northwest Corner Rule or the Minimum-Cost Method. This method involves starting from the northwest corner of the cost matrix and allocating shipments until the supply and demand constraints are met.

Explanation:

Let's calculate the allocations:

Start by allocating as much as possible from S1 to D1: 4000 barrels (the minimum requirement of D1).

Allocate the remaining demand of D1 (6000 - 4000 = 2000 barrels) from S2 to D1.

Allocate the remaining demand of D2 (6000 barrels) from S2 to D2.

The allocations would look as follows:

Outlet S1 to Distributor D1: 4000 barrels

Outlet S1 to Distributor D2: 0 barrels

Outlet S2 to Distributor D1: 2000 barrels

Outlet S2 to Distributor D2: 6000 barrels

To determine the minimum shipping cost, we multiply the quantity of oil allocated with the corresponding shipping cost and sum them up:

Total shipping cost = (4000 * $32) + (0 * $22) + (2000 * $25) + (6000 * $22)

= $128,000 + $0 + $50,000 + $132,000

= $310,000

Therefore, to minimize shipping costs, Outlet S1 should send 4000 barrels to Distributor D1.

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