Reclaiming the Solid Waste
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Case 2: Reclaiming the solid wasteINTRODUCTION This case talks about the Save-It company who operates the reclamation center which collects the solids waste of the four types which is mixed and forms the salable product. From this material three different types of the product are formed. Although this product formed have different proportion of the material with the different quality standards. Green Earth organization who owes the Save-It co, which is devoted in dealing with the environmental issues. So the profits of the Save-It co helps to support the organization. So the organization have raised $30000 per week as the contribution and grants to cover the entire treatment cost for the solid material. The board of directors of Green Earth has instructed the management of Save-It to divide this money among the materials in such a way that at least half of the amount available of each material is actually collected and treated.Within this restriction the management wants to determine the amount of each product grade to produce and the exact mix of materials to be used for each grade. The objective is to maximize the net weekly profit (total sales income minus total amalgamation cost), exclusive of the fixed treatment cost of $30,000 per week that is being covered by gifts and grants. FACTS AND FINDINGS The following are the tables which shows the cost of the amalgamation and selling price for each of the product is the given. And the other table shows the quantities available for collection and treatment each week, as well as the cost of treatment, for each type of material.PRODUCT DATA FOR SAVE-IT COMPANYGRADESPECIFICATIONSAMALGAMATIONCOST PER POUND($)SELLING PRICE PER POUND($)AMaterial 1: not more than 30% of the totalMaterial 2: not less than 40% of the totalMaterial 3: not more than 50% of the total Material 4: exactly 20% of the total3.008.50BMaterial 1: not more than 50% of totalMaterial 2: not less than 10% of the total Material 4: exactly 10% of the total2.507.00CMaterial 1: not more than 70% of the total2.005.50SOLID WASTE MATERIAL DATA FOR THE SAVE-IT COMATERIALPOUNDS PER WEEK AVAILABLETREATMENT COST PER POUND ($)ADDITIONAL RESTRICTIONS130003.00for each material,220006.00 At least half of the pounds per 340004.00Week available 410005.00Should be collected and treated$30000 per week should be used to treat these material
AnalysisThe problem could be solved through linear programing. Through which we would find our objective of maximizing the net weekly profit by selling the salable product.OBJECTIVE: To maximize the profit (by selling salable product)DECISION VARIABLE :Let X1 be material 1 of ALet X2 be material 2 of ALet X3 be material 3 of ALet X4 be material 4 of ALet X5 be material 1 of BLet X6 be material 2 of BLet X7 be material 3 of BLet X8 be material 4 of BLet X9 be material 1 of CLet X10 be material 2 of CLet X11 be material 3 of CLet X12 be material 4 of COBJECTIVE FUNCTION: To maximize profit, P= {8.50 * (X1+X2+X3+X4) + 7 * (X5+X6+X7+X8) + 5.50 * (X9+X10+X11+X12)} – {3 * (X1+X2+X3+X4) + 2.50 * (X5+X6+X7+X8) + 2 * (X9+X10+X11+X12)}Subject to constraints,MIXTURE SPECIFICATION: GRADE A0.70X1-0.30X2-0.30X3-0.30X4 <= 0-0.40X1+0.60X2-0.40X3-0.40X4>=0-0.50X1-0.50X2+0.50X3-0.50X4<=0-0.20X1-0.20X2-0.20X3+0.80X4=0GRADE B0.50X5-0.50X6-0.50X7-0.50X8<=0-0.10X5+0.90X6-0.10X7-0.10X8>=0-0.10X5-0.10X6-0.10X7+0.90X8=0GRADE C0.30X9-0.70X10-0.70X11-0.70X12<=0AVAILABILTYMATERIAL 1 : X1+X5+X9<=3000MATERIAL 2: X2+X6+X10<=2000MATERIAL 3: X3+X7+X11<=4000MATERIAL 4: X4+X8+X12<=1000ADDITIONAL RESTRICTIONMATERIAL 1 : X1+X5+X9>=1500MATERIAL 2: X2+X6+X10>=1000MATERIAL 3: X3+X7+X11>=2000MATERIAL 4: X4+X8+X12>=500TREATMENT COST OF MATERIAL3X1+6X2+4X3+5X4+3X5+6X6+4X7+5X8+3X9+6X10+4X11+5X12=3000Non-negativity function: Xi >= 0 Where, i= 1,2,3,4,,5,6,7,8,9,10,11,12 Now this would be solved through MS Excel;Variables X1X2X3X4X5X6X7X8X9X10X11X12profitSolution 41286044743025885181553518000035110Objective 666655554444