Introduction to Management Science 12th Edition by Bernard Taylor

Exercise 30

Suppose in Problem that the processing cost per unit at each plant is different because of different machinery, workers' abilities, overhead, and so on, according to the following table:
There are no differentiated costs at stage 5, the distribution center. Given a budget of $700,000, determine the maximum number of units that can be processed through the five-stage manufacturing process.
Problem
The Dynaco Company manufactures a product in five stages. Each stage of the manufacturing process is conducted at a different plant. The following network shows the five different stages and the routes over which the partially completed products are shipped to the various plants at the different stages:

Stage 5 (at node 10) is the distribution center in which final products are stored. Although each node represents a different plant, plants at the same stage perform the same operation. (For example, at stage 2 of the manufacturing process, plants 2, 3, and 4 all perform the same manufacturing operation.) The values accompanying the branches emanating from each node indicate the maximum number of units (in thousands) that a particular plant can produce and ship to another plant at the next stage. (For example, plant 3 has the capacity to process and ship 7,000 units of the product to plant 5.) Determine the maximum number of units that can be processed through the five-stage manufacturing process and the number of units processed at each plant.