Walsh’s management wants to determine how many tons of grape juice to ship from each of the vineyards to each of the plants, and the number of tons of each product to process at each plant. Thus, management needs a model that includes both the logistical aspects of this problem and the production processing aspects. It wants a solution that will minimize total costs, including the cost of transporting grape juice from the vineyards to the plants and the product processing costs. Help Walsh’s solve this problem by formulating a linear programming model and solve it using Excel.

Walsh’s Juice Company produces three products from unprocessed grape juice—bottled juice, frozen juice concentrate, and jelly. It purchases grape juice from three vineyards near the Great Lakes. The climate in this area is good for growing the concord grapes necessary to produce grape juice products. The grapes are harvested at the vineyards and immediately converted into juice at plants at the vineyard sites and stored in refrigerated tanks. The juice is then transported to four different plants in Virginia, Michigan, Tennessee, and Indiana, where it is processed into bottled grape juice, frozen concentrated juice, and jelly. Vineyard output typically differs each month in the harvesting season and the plants have different processing capacity