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(b) A plant manufactures three products, 1,2 and 3. Four production departments are involved. A product may be made through alternative routings. For example, product A can be manufactured through processing in departments I, II, and III, or in departments I, II and IV. Profit depends on the routing (see Table 1). The hours available for scheduling in the period to be planned are shown in the last row. At least 10 units of product 2 must be manufactured in the period. No more than 40 units of product 3 may be manufactured because of material limitations. Formulate a Linear Programming model for this