A plant can manufacture three products A, B, and C. The plant has four departments, I, II, III, and IV. Product A must be processed in departments I and II; product B in departments I, II, III, and IV; and product C in departments I, III, and IV. Departments I and II must each be scheduled for at least 100 h, while at least 1000 pieces of product A must be manufactured. Then, a purchase part used in the assembly of products A and C is scarce and only 3500 parts are available for the month. Two parts are used in each piece of product A and three parts are used in each piece of product C. Table 2 below contains the relevant information.

Identify the objective function, formalize the various constraints, and determine the most profitable product mix for the month.

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TABLE 2 OUTPUT RATE IN PIECES PER HOUR UNIT PROFIT PRODUCTION MIN CONSTR. DEPT DEPT DEPT DEPT PRODUCT II III IV MIN MAX A 20.00 40.00 0.00 0.00 3.10 1000 B 30.00 25.00 10.00 22.00 2.05 C 60.00 0.00 20.00 5.00 6.17 Available Hours 150 160 130 100 MIN 100 100 Source: Lynwood A. Johnson, Douglas C. Montgomery, Operations Research in Production Planning, Scheduling and Inventory Control, Exercise 3.3, p.168, Copyright 1974 by John Wiley and Sons, Inc.