Katherine Mofokeng is the owner of a recycling company that specialises in collecting and recycling paper...

 

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Katherine Mofokeng is the owner of a recycling company that specialises in collecting and recycling paper products. Katherine's company uses two different recycling processes to convert newspaper, mixed paper, white office paper and cardboard into paper pulp. The amount of paper pulp extracted from the recyclable materials and the cost of extracting the pulp differs depending on which recycling process is used. The following table summarises the recycling process: For example, every ton of newspaper subjected to recycling process 1 costs $13 and yields 0.9 tons of paper pulp. The paper pulp goes through other operations to be transformed into pulp for newsprint, packaging paper or print stock quality paper. The yields associated with transforming the recycled pulp into pulp for the final products is given in the following table: Material News Paper Mixed Paper White Office Paper Cardboard Pulp Source Recycling Process 1 Recycling Process 1 Recycling Process 1 Cost Per Ton ($) 13 A- 11 9 13 011 012 921 022 Newsprint Pulp Cost Per Ton ($) 5 6 Yield (%) 90 an a₂n 80 95 75 Recycling Process 2 6 8 Cost Per Ton ($) 12 13 10 14 Packaging Paper Pulp Yield Cost Per Ton Yield (%) ($) (%) 95 90 90 95 Yield 85 85 90 85 Print Stock Pulp Cost Per Ton ($) 8 7 Yield For example, a ton of pulp exiting recycling process 2 can be transformed into 0.95 tons of packaging paper pulp at a cost of $8. 90 Katherine currently has 70 tons of newspaper. 50 tons of mixed paper. 30 tons of white office paper and 40 tons of cardboard. She would like to determine the most efficient way of converting these materials into 60 tons of newsprint pulp, 40 tons of packaging paper pulp and 50 tons of print stock pulp. 95 a. Graphical representation of Recycling project as a generalized network flow problem (10 Marks) b. Formulate the problem as a linear programming problem. (See hint) (10 Marks) c. Use solver to determine the optimal allocation (10 Marks) Hint: Use the table of constraint coefficients for linear programming: OPR 371S Minor Test 5 Assessment 5 2022 Katherine Mofokeng is the owner of a recycling company that specialises in collecting and recycling paper products. Katherine's company uses two different recycling processes to convert newspaper, mixed paper, white office paper and cardboard into paper pulp. The amount of paper pulp extracted from the recyclable materials and the cost of extracting the pulp differs depending on which recycling process is used. The following table summarises the recycling process: For example, every ton of newspaper subjected to recycling process 1 costs $13 and yields 0.9 tons of paper pulp. The paper pulp goes through other operations to be transformed into pulp for newsprint, packaging paper or print stock quality paper. The yields associated with transforming the recycled pulp into pulp for the final products is given in the following table: Material News Paper Mixed Paper White Office Paper Cardboard Pulp Source Recycling Process 1 Recycling Process 1 Recycling Process 1 Cost Per Ton ($) 13 A- 11 9 13 011 012 921 022 Newsprint Pulp Cost Per Ton ($) 5 6 Yield (%) 90 an a₂n 80 95 75 Recycling Process 2 6 8 Cost Per Ton ($) 12 13 10 14 Packaging Paper Pulp Yield Cost Per Ton Yield (%) ($) (%) 95 90 90 95 Yield 85 85 90 85 Print Stock Pulp Cost Per Ton ($) 8 7 Yield For example, a ton of pulp exiting recycling process 2 can be transformed into 0.95 tons of packaging paper pulp at a cost of $8. 90 Katherine currently has 70 tons of newspaper. 50 tons of mixed paper. 30 tons of white office paper and 40 tons of cardboard. She would like to determine the most efficient way of converting these materials into 60 tons of newsprint pulp, 40 tons of packaging paper pulp and 50 tons of print stock pulp. 95 a. Graphical representation of Recycling project as a generalized network flow problem (10 Marks) b. Formulate the problem as a linear programming problem. (See hint) (10 Marks) c. Use solver to determine the optimal allocation (10 Marks) Hint: Use the table of constraint coefficients for linear programming: OPR 371S Minor Test 5 Assessment 5 2022

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