### Factory directly ships its toys to the destination country

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XYZ company manufactures toys in three different countries: S1, S2 and S3. It sells these toys in four countries: A, B, C and D. The following table shows the total requirement for each type of toy by country of manufacture:

 A B C D S1 10 40 60 10 S2 4 15 21 36 S3 31 20 14 16

XYZ is looking at two potential options:

Option 1. Direct shipment. Each factory directly ships its toys to the destination country. In this case, transportation cost is \$1.50 per lb-mile. Assume that each toy weighs 1 lb (one lb-mile indicates transportation effort to ship one pound weight over one mile distance).

Option 2. Via warehouse. In this case, a central warehouse is established. All shipments from S1, S2 and S3 go to the central warehouse. In the central warehouse, toys are repackaged by destination - that is, all toys needed for A are consolidated and shipped to A. Cost of transportation for in-bound units to the central warehouse is \$0.85 per lb-mile, and outbound transportation cost is \$1.30 per lb-mile.

The (x, y) coordinates for the factories and customers are given below:

 A B C D S1 S2 S3 x- coordinate 7 8 13 20 5 10 1 y- coordinate 4 15 12 12 13 14 5

Answer the following questions:

What is the total cost if direct shipments are used?

Should XYZ establish a central warehouse? If so, where should it be located? Justify or support your analysis with adequate computational analysis.

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