Introduction
Walsh’s Juice Company (the Company) produces three products from unprocessed grape juice – bottled juice, frozen juice concentrate, and jelly. Walsh’s management wants a solution that will minimize the total cost of transporting grape juice from vineyards to processing plants, and minimize product processing costs at those plants.

Analysis and Data
The Company purchases grape juice from three vineyards. Grapes are harvested at the vineyards and converted into juice at plants at the vineyard sites. The juice is then transported to four different plants in Virginia, Michigan, Tennessee, and Indiana, where it is processed into bottled grape juice, frozen juice concentrate, and jelly.

The Company’s management provided the following data for transportation costs from the vineyards to the plants, the unprocessed grape juice available at the vineyards, and the processing capacity of each plant; shown in the table below:

Each plant has different processing costs, mainly due to wage rates and age of the plants. The processing costs of each plant are shown in the table below:

Finally, the following information was provided: * The Company needs to process a total of 1,200 tons of bottled juice, 900 tons of frozen concentrate, and 700 tons of jelly at the four plants combined. * To process 1 ton of frozen concentrate requires 2 tons of unprocessed juice; 1 ton of jelly requires 1.5 tons of unprocessed juice, and 1 ton of bottled juice requires 1 ton of unprocessed juice. We will use a linear programming model and solve the model to determine the minimum cost of transporting grape juice from the vineyards to the plants, and the minimum product processing costs. Results and Conclusion There are three steps in developing a linear programming model. The first step is to identify the decision variables. This analysis