Question

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: 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 be found?

Answer 1

The student's problem pertains to optimizing shipping routes for grain to minimize freight costs, using principles of supply chain management to improve profitability. The scenario is akin to how falling gasoline prices can allow a messenger company to increase its service area and therefore its supply.

Step-by-step explanation:

The student is dealing with a problem that involves minimizing freight costs in a grain shipping business by creating an efficient shipping schedule. To achieve this, one must consider various transportation costs and methods, including rail and road, as well as understand how fluctuations in costs, such as those for gasoline, can affect overall profitability and operation scales. For instance, if gasoline prices fall, a messenger company can operate more efficiently by servicing a wider area, illustrating the impact of transportation costs on business operations. Similarly, the Moore & Harman Company can improve profitability by reducing their freight costs through optimal shipping route selection. While the specific shipping costs and locations are not detailed in the question, the key to answering it lies in applying principles of supply chain management to minimize costs while meeting customer demand.

To determine a shipping schedule that minimizes freight costs, we need to consider the shipping costs from the origins to Louisville and Cincinnati, and the costs from Louisville and Cincinnati to the destinations. We also need to take into account the demand at each location. The rail cars of grain that must be held at the origin until buyers can be found are the ones with the highest shipping costs to both Louisville and Cincinnati, as well as the highest costs from both Louisville and Cincinnati to the destinations.