A firm has established a distribution network for the supply of a raw material critical to its manufacturing. Currently there are three origins for this raw material, which must be shipped to three manufacturing plants. The current network has the following characteristics: Costs Plant 1 Plant 2 Plant 3 Supply
Raw material source 1 $6 $8 $9 400
Raw material source 2 $4 $7 $3 600
Demand 500 500 500 Supply < Demand

The firm has identified two potential sites for a third raw material source; these are identified as Candidate A and Candidate B. From A, the costs to ship would be $9 to Plant 1, $10 to Plant 2, and $12 to Plant 3. From B, these costs would be $11, $14, and $8. The new source, wherever it is located, will have a capacity of 500 units. Solve with the transportation method. Which site should be selected?

Candidate A should be selected due to lower costs

Explanation:

Cost with Candidate A = Sum (Cost of unit × Number of units)

Cost with Candidate A = 6(400) + 4(100) + 10(500) + 3(500)

Cost with Candidate A = $9300

(TABLE ATTACHED BELOW)

Cost with Candidate B = Sum (Cost of unit × Number of units)

Cost with Candidate B = 6(400) + 4(100) + 14(500) + 3(500)

Cost with Candidate B = $11300

In the solution we are supplying 500 units from Source 2 and Candidate B to Plant 3 and Plant 2 respectively. The cost per unit = 14+3 = $17. If we interchange the source to the plant the cost is 7+8 = $15

Optimal Cost with Candidate B = 6(400) + 4(100) + 8(500) + 7(500)

Optimal Cost with Candidate B = $10300

(TABLE ATTACHED BELOW)

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