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 recycler is currently trying to determine the best way of filling an order for 500 tons of newsprint pulp, 600 tons of packaging paper pulp, and 300 tons of print-stock quality pulp. The following table summarizes the yield for each kind of pulp recovered from each ton of recycled material.

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. Newspaper and cardboard cannot be converted to print-stock pulp using the techniques available to the recycler. As each material is recycled, it also produces a toxic sludge that the recycler must dispose of. The amount of toxic sludge (in pounds) created by processing a ton of each of the raw materials into each of the types of pulp is summarized in the following table. For instance, each ton of newspaper that is processed into newspaper pulp creates 125 pounds of sludge.

The cost 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 four raw materials that can be purchased, and their costs.

These processing costs include the cost of disposing of sludge. However, the managers of the recycling facility would prefer to minimize the amount of sludge created, and the total cost of filling the order.
a. Formulate an MOLP model for this problem and implement your model in a spreadsheet.
b. Determine the best possible value for each objective in the problem.
c. Determine the solution that minimizes the maximum percentage deviation from the optimal objective function values. What solution do you obtain?
d. Suppose that management considers minimizing costs to be twice as important as minimizing the amount of sludge produced. What solution does thissuggest?

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Recycling Yield Newsprint Packaging Print Stock 80% Newspaper 85% 80% д0% White PaperPaper9% 90% 80% 80% White Office Paper Cardboard 85% 70% Newspaper Mixed Paper White Office Paper Cardboard Sludge (Ibs.) Newsprint Packaging Print Stock 100 100 75 150 125 50 50 100 150 100 0 Processing Costs per Ton Newsprint Packaging Print Stock $11.00 $12.25 $ 7.75 $8.50 Purchase Cos Tons Newspaper Mixed Paper White Office Paper Cardboard $6.50 $9.75 apr$4.75 Per ion $15 $16 $19 $17 Available 600 500 300 400 $9.50 $8.50 $7.50