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4. Reclaiming Solid Waste (Blending Problem) The SAVE-IT COMPANY operates a reclamation center that collects four types of solid waste materials (1, 2, 3 & 4) and treats them so that they can be amalgamated into a salable product of three different grades (A...The Problem. Definition: grades depend on the mix of material used Determine the amount of each product grade to Material Pounds per Treatment week produce and the cost per Additional Restrictions available pound (5) exact mix of materials to be used 1 3,000 3.00 1. For each material, at least half of the for each grade while 2 2,000 4.00 pounds per week valable should be maximizing the net 3 4,000 selected and treated 4.00 2 4 1,000 weekly profit (total 5.00 $30,000 per week should be used to treat these materials. sales income minus ) mulation Selling Price total amalgamation Grade Specification Cast Pound Around cost, exclusive of 151 the fixed treatment cost of $30,000 per Material 1: Nat more than 30% of total Material 2: Not less than 40% of total week that is being 2.00 8.50 Maturala: Not more than 50% of total covered by gifts and Material 4 Exactly 20% of total grants.) 3 Material 1. Not more than 50% of total Material 2: Not less than 10% of total 2.50 7.00 Material 4: Exactly 10% of total Material: Not more than 70% of total 2.00 5.50 2 A 4. Reclaiming Solid Waste (Blending Problem) Decision variables X = number of pounds of material allocated to product grade i per week (where i = A,B,C and j = 1,2,3,4). The linear program is as follows: Max Z = 5.5 (Xx+ XA2+ XA2+ Xx4) + 4.5 (X31+Xg2+Xg3+Xp4) +3.5 (Xc1+X+Xcx+Xce) Subject to the following constraints: (1) Mixture specification: XAL S 0.3 (%A1+ x^2 + x + x) XA2 20.4 (XA1+ x2 + x^2 + x4) XA S 0.5 (XA1+ XA2+ x + XAa) XA4 = 0,2 (A + XA2+ XAg+ Xoa) 4. Reclaiming Solid Waste (Blending Problem) X1 50.5 (xs1+Xg2+X83+X34) 81 B3 Xay 20.1 (x +X2+Xa + a) X34 = 0.1 (XB1+Xg2+Xg3+X54) Xix 0.7 (x1+x2+x+1) (2) Availability of materials: XA1+ X1 + Xc S 3000 XA2+ x2 + x = 2000 XA3+ X3 + Xcz S 4000 4+ Nga + X31000 (3) Restrictions on amounts treated: XA1+ X: + X 1500 XA2+ Xs2 + Xc 2 1000 22 4. Reclaiming Solid Waste (Blending Problem) XA3+ X83 + Xc3 2 2000 XA4+ X94 + Xc4 2 500 (4) Restrictions on treatment cost: 3 (XA1+ Xi + x) + 6 (XA2+ XB2 + x) + 4 ( A3+ XB3 + 3cm) + 5 (X + XB4 + x) = 30,000 (5) Non-negativity constraints: XA1 ...............20