Reclaiming the Solid Waste
Essay by Pratham Goyal • February 16, 2016 • Case Study • 1,202 Words (5 Pages) • 1,499 Views
Case 2: Reclaiming the solid waste
INTRODUCTION
This case talks about the SaveIt 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 SaveIt co, which is devoted in dealing with the environmental issues. So the profits of the SaveIt 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 SaveIt 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 $30,000 per week that is being covered by gifts and grants.
FACTS AND FINDINGS
The following are the tables which shows the cost of the amalgamation and selling price for each of the product is the given. And the other table shows the quantities available for collection and treatment each week, as well as the cost of treatment, for each type of material.
PRODUCT DATA FOR SAVEIT COMPANY
GRADE  SPECIFICATIONS  AMALGAMATION COST PER POUND($)  SELLING PRICE PER POUND($) 
A  Material 1: not more than 30% of the total  
Material 2: not less than 40% of the total  
Material 3: not more than 50% of the total  
Material 4: exactly 20% of the total  3.00  8.50  
B  Material 1: not more than 50% of total  
Material 2: not less than 10% of the total  
Material 4: exactly 10% of the total  2.50  7.00  
C  Material 1: not more than 70% of the total  2.00  5.50 
SOLID WASTE MATERIAL DATA FOR THE SAVEIT CO
MATERIAL  POUNDS PER WEEK AVAILABLE  TREATMENT COST PER POUND ($)  ADDITIONAL RESTRICTIONS 
1  3000  3.00  for each material, 
2  2000  6.00  At least half of the pounds per 
3  4000  4.00  Week available 
4  1000  5.00  Should be collected and treated 
$30000 per week should be used to treat these material 
Analysis
The 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 A
 Let X2 be material 2 of A
 Let X3 be material 3 of A
 Let X4 be material 4 of A
 Let X5 be material 1 of B
 Let X6 be material 2 of B
 Let X7 be material 3 of B
 Let X8 be material 4 of B
 Let X9 be material 1 of C
 Let X10 be material 2 of C
 Let X11 be material 3 of C
 Let X12 be material 4 of C
OBJECTIVE 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 A
 0.70X10.30X20.30X30.30X4 <= 0
 0.40X1+0.60X20.40X30.40X4>=0
 0.50X10.50X2+0.50X30.50X4<=0
 0.20X10.20X20.20X3+0.80X4=0
GRADE B
 0.50X50.50X60.50X70.50X8<=0
 0.10X5+0.90X60.10X70.10X8>=0
 0.10X50.10X60.10X7+0.90X8=0
GRADE C
 0.30X90.70X100.70X110.70X12<=0
AVAILABILTY
 MATERIAL 1 : X1+X5+X9<=3000
 MATERIAL 2: X2+X6+X10<=2000
 MATERIAL 3: X3+X7+X11<=4000
 MATERIAL 4: X4+X8+X12<=1000
ADDITIONAL RESTRICTION
 MATERIAL 1 : X1+X5+X9>=1500
 MATERIAL 2: X2+X6+X10>=1000
 MATERIAL 3: X3+X7+X11>=2000
 MATERIAL 4: X4+X8+X12>=500
TREATMENT COST OF MATERIAL
 3X1+6X2+4X3+5X4+3X5+6X6+4X7+5X8+3X9+6X10+4X11+5X12=3000
Nonnegativity 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 
 X1  X2  X3  X4  X5  X6  X7  X8  X9  X10  X11  X12  profit 
Solution 
 412  860  447  430  2588  518  1553  518  0  0  0  0  35110 
Objective 
 6  6  6  6  5  5  5  5  4  4  4  4 

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