solution

Constraints are on machine capacities. They can be expressed as follows: Machine A, is used to manufacture product I through combinations (A,B),(A,B),(A, B3) with associated variables X1, X2 and xz and to manufacture product 2 through (A,B) with associated variable xy. The total time demand on A, is 4x + 4×2 + 4×3 + 6xy per week and this should not exceed 5,000 minutes. Similarly, A2 is used to manufacture product I through combinations (Az. B), (2. B) and (A2. By) with associated variables x4. rs and to product 2 through combination (A2, B,) with associated variable xg and product 3 through combination (A2. B) with associated variable xy. Thus the total weekly time demand on A, is 5×4 + 5×5 + 5x + 7×9 + 11x, per week and this should not exceed 10,000 minutes. Likewise, total time demand on B, is 7x + 7×4 + 8×7 + 8xg, on B, is 8×2 + 8x, and on B, is 3x + 3×6 + 7x, which should not exceed 8,000, 4,000 and 5,600 minutes per week respectively. Thus the various constraints can we written as 4x) + 4×2 + 4x + 6×7 s 5,000, 5×4 + 5×3 + 5×6 + 7xg + 11x9s 10,000 + 8x, + 8×8 S 8,000 s 4,000, 3×3 + 7×9 S 5,600, where x1, x2, … Xy, each 20. EXAMPLE 2.6-19 (Product Mix Problem) A firm manufactures two items. It purchases castings which are then machined, bored and polished. Castings for items A and B cost 2 and 3 respectively and are sold at 5 and 6 each respectively . Running costs of the three machines are * 20, < 14 and 17.50 per hour respectively. Capacities of the machines are Part A Part B Machining capacity 25/hr 40/hr Boring capacity 35/hr Polishing capacity 35/hr 25/hr Formulate the L.P. model to determine the product mix that maximizes the profit.