Question
Wheat is harvested in Nebraska and Colorado and then must be shipped to grain elevators in Kansas City, Omaha, and Des Moines. These Kansas City,
Wheat is harvested in Nebraska and Colorado and then must be shipped to grain elevators in Kansas City, Omaha, and Des Moines. These Kansas City, Omaha, and Des Moines transhipment points then had to ship products to Chicago, St. Louis, and Cincinnati.
Wheat growers in Nebraska and Colorado have outputs of 300 units, respectively, while demand in Chicago, St. Louis, and Cincinnati is 200, 100, and 300 units. Farmers cannot ship to the endpoint directly, and transhipment points cannot send to each other.
Below is a table of costs for shipping grain from one point to another.
Set up a transshipment system for the number of units of wheat that must be shipped from one point to another, provided that the cost of shipping wheat is minimum.
\begin{tabular}{|l|l|l|l|l|l|l|l|} \hline COSt & Chicago & St.Louis & Cincinnati & KansasCity & Omaha & DesMoines & Supply \\ \hline Nebraska & 1000 & 1000 & 1000 & 16 & 10 & 12 & 300 \\ \hline Colorado & 1000 & 1000 & 1000 & 15 & 14 & 17 & 300 \\ \hline Kansas City & 6 & 8 & 10 & 0 & 1000 & 1000 & 600 \\ \hline Omaha & 7 & 11 & 11 & 1000 & 0 & 1000 & 600 \\ \hline Des Moines & 4 & 5 & 12 & 1000 & 1000 & 0 & 600 \\ \hline Demand & 200 & 100 & 300 & 600 & 600 & 600 & \\ \hline \end{tabular} \begin{tabular}{|l|l|l|l|l|l|l|l|} \hline COSt & Chicago & St.Louis & Cincinnati & KansasCity & Omaha & DesMoines & Supply \\ \hline Nebraska & 1000 & 1000 & 1000 & 16 & 10 & 12 & 300 \\ \hline Colorado & 1000 & 1000 & 1000 & 15 & 14 & 17 & 300 \\ \hline Kansas City & 6 & 8 & 10 & 0 & 1000 & 1000 & 600 \\ \hline Omaha & 7 & 11 & 11 & 1000 & 0 & 1000 & 600 \\ \hline Des Moines & 4 & 5 & 12 & 1000 & 1000 & 0 & 600 \\ \hline Demand & 200 & 100 & 300 & 600 & 600 & 600 & \\ \hline \end{tabular}Step by Step Solution
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