Production Planning 1 – A paperrecycling plant processes box board, tissue paper, newsprint and book paper into pulp that can be used to produce four grades of recycled paper (grades 1, 2, 3 and 4).
The prices per ton and the pulp contents of the four inputs are shown in the table. Two methods, de-inking and asphalt dispersion, can be used to process the four inputs into pulp. It costs $20 to de-ink a ton of any input. The process of de-inking removes 9% of the input’s pulp, leaving 91% of the original pulp. It costs $16 to apply asphalt dispersion to a ton of material. The asphalt dispersion process removes 22% of the input’s pulp. At most, 4,000 tons of input can be run through the asphalt dispersion process or the de-inking process.
Grade 1 paper can only be produced with newsprint or book paper pulp; grade 2 paper only with book paper, tissue paper, or box board pulp; grade 3 paper only with newsprint, tissue paper, or box board pulp; and grade 4 from any type. To meet its current demands, the company needs 500 tons of pulp for grade 1 paper, 500 tons of pulp for grade 2 paper, 600 tons of pulp for grade 3 paper; and 200 tons of grade 4. Formulate and solve the problem to minimize the cost of meeting the demands for pulp.
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