Please turn in the following problem. No need to solve the IP$.$

Homework problem: Distribution network for agricultural products

The Moore $\backslash$& 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 shipping 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. A total of $15$ carloads of grain have been sold to the customers. The locations and the amounts sold to customers are as follows:

All shipments must be routed through a grain processing center at either Louisville or Cincinnati. Shown below are the shipping costs per rail carload of grain from the origins to Louisville and Cincinnati and the costs to ship from the two hubs to the final customer destinations.

Construct a distribution network diagram for this problem.

Formulate an integer program for the determination of the optimal shipping plan with the objective of minimizing total transportation cost within the distribution network.

Hint: check total supply capacity and total customer demand before you proceed.