A canned food manufacturer has its manufacturing plants in three locations across a state. Their product has to be transported to three central distribution centers, which in turn disperse the goods to seventy-two stores across the state. Which of the following is most likely to be the objective function in this scenario?

a. minimizing the quantity of goods distributed across the stores

b. minimizing the cost of shipping goods from the plant to the store

c. decreasing the cost of their raw material sourcing

d. increasing the number of goods manufactured at the plant

b. minimizing the cost of shipping goods from the plant to the store

Explanation:

If we were to devise a linear program for this case, the most likely objective function would be to minimize the cost of shipping from the plants to the stores, because this is a key aspect to the operation since it can become a costly bottleneck.

While there are three plants, and three stores, this does not mean that costs will be optimized if the same number of goods and produced in each plant, and transported from each plant to a designated store. In fact, it is likely that each plant produces a different amount of goods, which further complicates the problem.

For this reason, it is necessary to find the best combination of shipped goods, from each plant, to each store.