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A factory produces 3 products, A, B and C. Four sections are available for production. Products can be produced following alternative routes. For example, product A can be produced in sections I, II, III or I, II, IV (in a flow shop). Profitability ratios depend on these routes. Required data is given in the table below. Product Alternative routes A 1 2 B 1 2 3 1 Available hours Production times per unit Section Section Section Section I II III IV 0,21 1,15 3,20 0,21 1,15 2,75 1,30 2,20 1,30 1,60 1,30 2,40 4,00 2,60 1,00 160 140 150 120 Profitability per unit ($) 6,00 5,90 10,00 11,50 9,70 8,50 - - The available hours scheduled for the planning period are shown in the last row. At least 10 units should be produced from product B during the planning period. Due to some material constraints, product C cannot be produced in more than 40 units. Develop the linear programming formulation of the problem in order to determine how much production to be produced from each unit during the planning period. (20p)