Reference no: EM1313979
Paper Recycling Company Exercise:
A paper recycling company converts newspaper, mixed paper, white office paper, and cardboard into pulp for newsprint, packaging paper, and print stock quality paper. The following table summarizes the yield for each kind of pulp recovered from each ton of recycled material.
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Recycling Yield
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Newsprint
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Packaging
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Print Stock
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Newspaper
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85%
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80%
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Mixed Paper
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90%
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80%
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70%
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White Office Paper Cardboard
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90%
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85%
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80%
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Cardboard
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80%
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70%
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For instance, a ton of newspaper can be recycled using a technique that yields 0.85 tons of newsprint pulp. Alternatively, a ton of newspaper can be recycled using a technique that yields 0.80 tons of packaging paper. Similarly, a ton of cardboard can be recycled to yield 0.80 tons of newsprint or 0.70 tons of packaging paper pulp. Note that newspaper and cardboard cannot be converted to print stock pulp using the techniques available to the recycler.
The costs of processing each ton of raw material into the various types of pulp is summarized in the following table, along with the amount of each of the for raw materials that can be purchased and their costs.
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Processing Costs per Ton
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Purchase Cost per Ton
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Tons Available
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Newsprint
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Packaging
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Print Stock
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Newspaper
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$6.5
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$11.00
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-
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$15
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600
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Mixed Paper
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$9.75
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$12.25
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$9.50
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$16
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500
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White Office Paper
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$4.47
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$7.75
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$8.50
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$19
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300
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Cardboard
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$7.50
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$8.50
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-
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$17
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400
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The recycler wants to determine the least costly way of producing 500 tons of newsprint pulp, 600 tons of packaging pulp, and 300 tons of print stock quality pulp.
(a) Develop a linear optimization spreadsheet model to solve the recycler's problem. (Make sure to document your model sufficiently (i.e., decision variables, constraints, objective etc) so that it is clear what your model is without requiring the instructor to go into Solver!)
(b) What is the cost of the optimal solution?
(c) What is the optimal strategy for producing 500 tons of newsprint pulp, 600 tons of packaging pulp, and 300 tons of print stock quality pulp at minimum cost?
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