Recovery for each type of raw weight of raw material

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(Recovery for each type of raw material*Corresponding weight of raw material to be ordered per batch) £ 4,000 Kgs per batch (or 4 Tons per batch) \ (0.84*T + 0.74*R + 0.85*S + 0.94*L + 0.97*I + 0.25*H + 0.95*P) £ 4 Tons (per batch) * B \ (0.84*T + 0.74*R + 0.85*S + 0.94*L + 0.97*I + 0.25*H + 0.95*P) – 4B £ 0 (b) Constraint on the minimum quantity (in Tons) of raw material per batch
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Minimum quantity (in tons) of Tasla, Rangeen, Imported Scrap and High Carbon that can be used in a batch is 0% \ (T / T RMT )*100 ³ 0; \ (R / T RMT )*100 ³ 0; \ (I / T RMT )*100 ³ 0; \ (H / T RMT )*100 ³ 0 \ T ³ 0 [Min Tasla constraint] R ³ 0 [Min Rangeen constraint] I ³ 0 [Min Imported Scrap constraint] H ³ 0 [Min High Carbon constraint] Minimum quantity of Sponge that can be used in a batch is 10% \ (S / T RMT )*100 ³ 10 \ 9*S – (T + R + L + I + H + P) ³ 0 [Min Sponge constraint] Minimum quantity of Local Scrap that can be used in a batch is 15% \ (L / T RMT )*100 ³ 15 \ 17*L – 3*(T + R + S + I + H + P) ³ 0 [Min Local Scrap constraint] Minimum quantity of Pig Iron that can be used in a batch is 5% \ (PI / T RM )*100 ³ 5 \ 19*P – (T + R + S + I + H + L) ³ 0 [Min Pig Iron constraint] (c) Constraint on the maximum quantity (in Tons) of raw material per batch Maximum quantity of Tasla that can be used in a batch is 50% \ (T / T RMT )*100 £ 50 \ -T + R + S + L + I + H + P ³ 0 [Max Tasla constraint] Similarly for the other raw materials, (R / T RMT )*100 £ 25 \ -3*R + T + S + L + I + H + P ³ 0 [Max Rangeen constraint] (S / T RMT )*100 £ 50 \ T + R - S + L + I + H + P ³ 0 [Max Sponge constraint] (L / T RMT )*100 £ 80 \ -L + 4*(T + R + S + I + H + P) ³ 0 [Max Local Scrap constraint] (I / T RMT )*100 £ 80 \ -I + 4*(T + R + S + L + H + P) ³ 0 [Max Imported Scrap constraint] (H / T RMT )*100 £ 20 \ -4*H + T + R + S + L + I + P ³ 0 [Max High Carbon constraint] (P / T RMT )*100 £ 10 \ -9*P + T + R + S + L + I + H ³ 0 [Max Pig Iron constraint] (d) Constraint on the total time (in hours) for production in a month Time for production in a month = [0.2 + (0.3 * Total Raw material weight in tons per batch/B)] * B £ 600 Hrs = 0.3 (T + R + S + L + I + H + P) + 0.2 B + £ 600 (e) Constraint on the Maximum Availability of Raw Material During the Following Month We assume that the quantity of raw material available in the following month to produce requisite finished product that would optimise profit would be much lesser than the maximum available quantity of the raw materials. Therefore, presently, the maximum availability of raw material during the following month is not being considered as constraint while optimising the profit for a batch production. (f) Un-constrained Variables
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Weights of all raw materials would be ³ 0 and also the number of batches produced in a month would be ³ 0 \ T ³ 0, R ³ 0, S ³ 0, L ³ 0, I ³ 0, H ³ 0, P ³ 0 & B ³ 0 The LP Model thus obtained has been solved by Simplex LP method using the Excel Solver. Based on the solution of the solver, following are calculated:- Raw Material Rate/Ton (INR) Recovery Min per Batch (% of Raw Material) Max per Batch (% of Raw Material) Max per Month (Ton) Weight of Raw Materials (in Tons) per Month Cost (INR) of Raw Materials for a Month Weight of Steel Produced (in tons) per Month Tasla 17,000 0.84 0% 50% 800 789.88 13427923.65 663.4974036 Rangeen 13,600 0.74 0% 25% 500 438.82 5967966.06 324.7275653 Sponge 17,800 0.85 10% 50% 1,000 175.53 3124405.76 149.1991516 Local Scrap 20,000 0.94 15% 80% 1,000 263.29 5265852.41 247.4950633 Imported Scrap 23,000 0.97 0% 80% 1,500 0.00 0.00 0 HC 2,500 0.25 20% 300 0.00 0.00 0 Total 1755.28 29576537.70 1468.30 Cost of Electricity per Month = 7177506.034
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