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A manufacturing engineer facing the problem of reducing the costs of production in his department, decided to see whether he can reduce the number of work stations involved in the production of a certain product. The final product consists of 6 components each of which is currently fabricated within a single workstation and then added to the product as it is passed through these stations. Even though more than one of these components may be fabricated in any one station, there is a limit of 16 minutes on how long the product can stay at any given station. In addition, due to the geometry of the parts, some components cannot be added unless others have been previously attached. (see below. This type of restriction is sometimes referred to as a a precedence relation.) Assembly Component (1) Predecessors Time Required for Assembly (minutes) (t) 9 3 5 7 3 8 1 2 3 4 5 6 2 + 1,3 The objective is to formulate this problem as an integer programming problem, the solution of which will correlate the assembly of the components with the minimum number of workstations