u 3-3 Formulate the following problem as a linear programming problem. Be certain to define the variables and show the objective function and the constraints. 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 depart- ments I and II: product B in departments I, II, III, and IV; and product C in departments 1, III, and IV. The problem is to determine the most profitable product mix for the plant during the next month. Relevant data are the following: OUTPUT RATE IN PIECES PER HOUR PRODUCT PROFIT PER PIECE DEPT. I DEPT 11 DEPT. III DEPT. IV B C 20 30 60 40 25 10 20 22 5 $3.10 2.05 6.17 Available Hours 150 160 130 100 Production Planning --Static Models 168 Departments I and II must each be scheduled for at least 100 hours. At least 1000 pieces of product A must be manufactured. A purchased part used in the assembly of products A and C is scarce-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. O AL e