The Moore & Harman Company is in the business of buying and selling grain. An important aspect of the company€™s business is arranging for the purchased grain to be shipped to customers. If the company can keep freight costs low, profitability will improve.
The company recently purchased three rail cars of grain at Muncie, Indiana; six rail cars at Brazil, Indiana; and five rail cars at Xenia, Ohio. Twelve carloads of grain have been sold. The locations and the amount sold at each location are as follows:
Number of
Location Rail Car Loads
Macon, GA ......... 2
Greenwood, SC ........ 4
Concord, SC ........ .. 3
Chatham, NC ......... 3
All shipments must be routed through either Louisville or Cincinnati. Shown are the shipping costs per bushel (in cents) from the origins to Louisville and Cincinnati and the costs per bushel to ship from Louisville and Cincinnati to the destinations.

Determine a shipping schedule that will minimize the freight costs necessary to satisfy demand. Which (if any) rail cars of grain must be held at the origin until buyers can befound?

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From Muncie Brazil Louisville Cincinnati 6Cost per bushel from Muncie to Cincinnati is 6e 0 Macon Greenwood Louisville Cincinnati Concord 34 28 Chatham 32 24 57 35 Cost per bushel from Cincinnati to Greenwood is 35¢