a. Formulate this problem in linear programming terms by identifying all the activities, resources, benefits, and fixed requirements that lurk within it.

b. Formulate and solve a spreadsheet model for this linear programming problem.

c. Express this linear programming model in the spreadsheet in algebraic form?

The Save-It Company operates a reclamation center that collects four types of solid waste materials and then treats them so that they can be amalgamated (treating and amalgamating are separate processes) into a salable product. Three different grades of this product can be made, depending on the mix of the materials used. (See the first table.) Although there is some flexibility in the mix for each grade, quality standards specify the minimum or maximum amount of the materials allowed in that product grade. (This minimum or maximum amount is the weight of the material expressed as a percentage of the total weight for that product grade.) For each of the two higher grades, a fixed percentage is specified for one of the materials. These specifications are given in the first table along with the cost of amalgamation and the selling price for each grade.

The reclamation center collects its solid waste materials from some regular sources and so is normally able to maintain a steady rate for treating them. The second table 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 Company is solely owned by Green Earth, an organization that is devoted to dealing with environmental issues; Save-It's profits are all 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 the second table.

Within the restrictions specified in the two tables, management wants to allocate the materials to product grades so as to maximize the total weekly profit (total sales income minus total amalgamation cost).

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Amalgamation Cost per Pound Selling Price per Pound Grade Specification 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 Material 1: Not more than 50% of the total Material 2: Not less than 10% of the total Material 4: Exactly 10% of the total Material 1: Not more than 70% of the total $3.00 $8.50 2.50 7.00 5.50 2.00 Available Pounds/Week Treatment Cost per Pound Material Additional Restrictions 3,000 2,000 4,000 1,000 $3.00 6.00 4.00 5.00 1. For each material, at least half of the pounds/week available should be collected and treated. 2. $30,000 per week should be used to treat these materials. 4