A paper-recycling plant processes box board, tissuepaper, newsprint, and book paper into pulp that can be usedto produce three grades of recycled paper (grades 1, 2, and3). The prices per ton and the pulp contents of the fourinputs are shown in Table 82. Two methods, de-inking andasphalt dispersion, can be used to process the four inputsinto pulp. It costs $20 to de-ink a ton of any input. Theprocess of de-inking removes 10% of the input’s pulp,leaving 90% of the original pulp. It costs $15 to applyasphalt dispersion to a ton of material. The asphalt dispersionprocess removes 20% of the input’s pulp. At most, 3,000tons of input can be run through the asphalt dispersionprocess or the de-inking process. Grade 1 paper can only beproduced with newsprint or book paper pulp; grade 2 paper,only with book paper, tissue paper, or box board pulp; andgrade 3 paper, only with newsprint, tissue paper, or boxboard pulp. To meet its current demands, the company needs500 tons of pulp for grade 1 paper, 500 tons of pulp forgrade 2 paper, and 600 tons of pulp for grade 3 paper.Formulate an LP to minimize the cost of meeting thedemands for pulp. TAB LE 82Input Cost ($) Pulp Content (%)Box board 5 15Tissue paper 6 20Newsprint 8 30Book paper 10 40
A paper-recycling plant processes box board, tissue
paper, newsprint, and book paper into pulp that can be used
to produce three grades of recycled paper (grades 1, 2, and
3). The prices per ton and the pulp contents of the four
inputs are shown in Table 82. 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 10% of the input’s pulp,
leaving 90% of the original pulp. It costs $15 to apply
asphalt dispersion to a ton of material. The asphalt dispersion
process removes 20% of the input’s pulp. At most, 3,000
tons of input can be run through the asphalt dispersion
process or the de-inking process. Grade 1 paper can only be
produced with newsprint or book paper pulp; grade 2 paper,
only with book paper, tissue paper, or box board pulp; and
grade 3 paper, only with newsprint, tissue paper, or box
board pulp. To meet its current demands, the company needs
500 tons of pulp for grade 1 paper, 500 tons of pulp for
grade 2 paper, and 600 tons of pulp for grade 3 paper.
Formulate an LP to minimize the cost of meeting the
demands for pulp.
TAB LE 82
Input Cost ($) Pulp Content (%)
Box board 5 15
Tissue paper 6 20
Newsprint 8 30
Book paper 10 40
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