As legend has it, Buddhist monks trained monkeys to deftly gather the youngest leaves from the tops of wild tea trees. The monkey -harvested leaves are unbroken and evenly sized to create the finest oolong tea in the world
There are five plantations that use monkeys for this task and four tea centers where the leaves must be shipped. The cost to send a kilogram of leaves from each plantation to each tea center is shown in the table. Note that supply equals demand in this scenario. What is the optimal shipping scheme such that the total transportation cost is minimized?
Tea House 1 Tea House 2 Tea House 3 Tea House 4 Supply
Monkey 1 $12 $13 $23 $15 400
Monkey 2 $6 $17 $11 $4 400
Monkey 3 $6 $14 $13 $19 300
Monkey 4 $8 $10 $6 $8 200
Monkey 5 $21 $22 $5 $21 200
Demand 500 350 250 400 1500
The optimal tableau is:
Tea House 1 Tea House 2 Tea House 3 Tea House 4
Monkey 1 50 350 0 0
Monkey 2 0 0 0 400
Monkey 3 300 0 0 0
Monkey 4 150 0 50 0
Monkey 5 0 0 200 0
The monks' total cost of this solution is $11,050.
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