The SAVE-IT COMPANY operates a reclamation center that collects four types of solid waste materials and treats them so that they can be amalgamated into a salable product. (Treating and amalgamating are separate processes.) Three different grades of this product can be made (see the first column of Table 1), depending upon the mix of the materials used. Although there is some flexibility in the mix for each grade, quality standards may specify the minimum or maximum amount allowed for the proportion of a material in the product grade. (This proportion is the weight of the material expressed as a percentage of the total weight for the product grade.) For each of the two higher grades, a fixed percentage Table 1 Grade A B с Specification Material 1: Not more than 30% of total Material 2: Not less than 40% of total Material 3: Not more than 50% of total Material 4: Exactly 20% of total Material 1: Not more than 50% of total Material 2: Not less than 10% of total Material 4: Exactly 10% of total Material 1: Not more than 70% of total Amalgamation Cost per Pound (S) 3.00 2.50 2.00 Selling Price per Pound (S) 8.50 7.00 5.50 is specified for one of the materials. These specifications are given in Table 1 along with the cost of amalgamation and the selling price for each grade. The reclamation center collects its solid waste materials from regular sources and so is normally able to maintain a steady rate for treating them. Table 2 gives the quantities available for collection and treatment each week, as well as the cost of treatment, for each type of material. The Save-It Co. is solely owned by Green Earth, an organization devoted to dealing with environmental issues, so Save-It's profits are used to help support Green Earth's activities. Green Earth has raised contributions and grants, amounting to $30,000 per week, to be used exclusively to cover the entire treatment cost for the solid waste materials. 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. These additional restrictions are listed in Table 2
The SAVE-IT COMPANY operates a reclamation center that collects four types of solid waste materials and treats them so that they can be amalgamated into a salable product. (Treating and amalgamating are separate processes.) Three different grades of this product can be made (see the first column of Table 1), depending upon the mix of the materials used. Although there is some flexibility in the mix for each grade, quality standards may specify the minimum or maximum amount allowed for the proportion of a material in the product grade. (This proportion is the weight of the material expressed as a percentage of the total weight for the product grade.) For each of the two higher grades, a fixed percentage Table 1 Grade A B с Specification Material 1: Not more than 30% of total Material 2: Not less than 40% of total Material 3: Not more than 50% of total Material 4: Exactly 20% of total Material 1: Not more than 50% of total Material 2: Not less than 10% of total Material 4: Exactly 10% of total Material 1: Not more than 70% of total Amalgamation Cost per Pound (S) 3.00 2.50 2.00 Selling Price per Pound (S) 8.50 7.00 5.50 is specified for one of the materials. These specifications are given in Table 1 along with the cost of amalgamation and the selling price for each grade. The reclamation center collects its solid waste materials from regular sources and so is normally able to maintain a steady rate for treating them. Table 2 gives the quantities available for collection and treatment each week, as well as the cost of treatment, for each type of material. The Save-It Co. is solely owned by Green Earth, an organization devoted to dealing with environmental issues, so Save-It's profits are used to help support Green Earth's activities. Green Earth has raised contributions and grants, amounting to $30,000 per week, to be used exclusively to cover the entire treatment cost for the solid waste materials. 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. These additional restrictions are listed in Table 2
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
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Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
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Transcribed Image Text:The SAVE-IT COMPANY operates a reclamation center that collects four types of solid
waste materials and treats them so that they can be amalgamated into a salable product.
(Treating and amalgamating are separate processes.) Three different grades of this product
can be made (see the first column of Table 1), depending upon the mix of the materials
used. Although there is some flexibility in the mix for each grade, quality standards may
specify the minimum or maximum amount allowed for the proportion of a material in the
product grade. (This proportion is the weight of the material expressed as a percentage of
the total weight for the product grade.) For each of the two higher grades, a fixed percentage
Table 1
Grade
A
B
с
Specification
Material 1: Not more than 30% of total
Material 2: Not less than 40% of total
Material 3: Not more than 50% of total
Material 4: Exactly 20% of total
Material 1: Not more than 50% of total
Material 2: Not less than 10% of total
Material 4: Exactly 10% of total
Material 1: Not more than 70% of total
Amalgamation
Cost per Pound (S)
3.00
2.50
2.00
Selling Price
per Pound (S)
8.50
7.00
5.50
is specified for one of the materials. These specifications are given in Table 1 along with
the cost of amalgamation and the selling price for each grade.
The reclamation center collects its solid waste materials from regular sources and so is
normally able to maintain a steady rate for treating them. Table 2 gives the quantities
available for collection and treatment each week, as well as the cost of treatment, for each
type of material.
The Save-It Co. is solely owned by Green Earth, an organization devoted to dealing
with environmental issues, so Save-It's profits are used to help support Green Earth's
activities. Green Earth has raised contributions and grants, amounting to $30,000 per
week, to be used exclusively to cover the entire treatment cost for the solid waste materials.
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. These additional restrictions
are listed in Table 2
Transcribed Image Text:Table 2
Material
1
2
3
4
Pounds per
Week Available
3,000
2,000
4,000
1,000
Treatment Cost
per Pound (5)
3.00
6.00
4.00
5.00
Additional Restrictions
1. For each material, at least half of the
pounds per week available should be
collected and treated.
2. $30,000 per week should be used
to treat these materials.
Within the restrictions specified in Tables 1 and 2, 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.
Formulate the blended LP for this problem showing
1) The Objective function
2) The mixture specifications from Table 1
3) The availability of materials (2nd column Table 2)
4) Restrictions on the amount treated (Note 1 in 4th column Table 2(
5) Restriction on treatment cost(Note 2 in 4th column table 2(
6) Non negativity constraints(
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