Three products A, B, and C are produced in a plant, and for a given period there is the problem of deciding how much of each produc t to produce. Table 1 below contains information on the production process, profitability, and sales potential of each item. Identify the objective function, formalize the various constraints, and formulate the linear programming model.

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Exercises TABLE 1 409 PROCESSING TIME IN HOURS PER UNIT UNIT PROFIT E SALES CAPACITY DEPT DEPT DEPT PRODUCT I II III INSPECTION SHIPPING MIN MAX A 0.14 0.60 0.20 0.04 0.10. 42 150 250 B 0.10 0.40 0.20 0.04 0.10 40 200 400 0.20 0.10 0.04 0.12 36 360 500 Hours of 160 320 160 80 80 Capacity Source: Lynwood A. Johnson, Douglas C. Montgomery, Operations Research in Production Planning, Scheduling and Inventory Control, Exercise 3.1, p. 167, Copyright 1974 by John Wiley and Sons, Inc.