A soft drink manufacturing company has three factories-one in Orlando, one in Tampa, and one in Port St. Lucie-that supply soft drink bottles to three warehouses located in the city of Miami. The associated per-unit transportation cost between the factories and the warehouses is provided in the table below.
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Transportation Costs ($)
Factories/Warehouse (W)W1
W2
W3
Orlando7
4
5
Tampa7
6
4
Port St. Lucie5
5
6
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The factory in Orlando has a capacity of 14,000 units.The factory in Tampa has a capacity of 25,000 units.The factory in Port St. Lucie has a capacity of 23,000 units.The requirements of the warehouses are:
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Warehouse
Requirement (Bottles)
W1
18,000
W2
19,000
W3
22,000
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Determine how much of the company's production should be shipped from each factory to each warehouse in order to minimize the total transportation cost?
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What will be an ideal response?
x12: number of bottles shipped from Orlando to W2
.
.
.
x33: number of bottles shipped from Port St. Lucie to W3
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Min 7x11 + 4x12 + 5x13 + 7x21 + 6x22 + 4x23 + 5x31 + 5x32 + 6x33
s.t.
x11 + x12 + x13 ? 14000
x21 + x22 + x23 ? 25000
x31 + x32 + x33 ? 23000
x11 + x21 + x31 = 18000
x12 + x22 + x32 = 19000
x13 + x23 + x33 = 22000
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x11, x12, x13, …, x33³ 0
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