Chapter 3, Problem 52RP

Explanation of Solution

LP to minimize the cost of meeting the demands for pulp:

• Assume the following,
  • Let “Ns” be the tons of newsprint bought.
  • Let “Bk” be the tons of book paper bought.
  • Let “${\text{Bx}}_1$” be the tons of boxboard sent via de-inking.
  • Let “${\text{Tis}}_1$” be the tons of tissue sent via de-inking.
  • Let “${\text{Ns}}_1$” be the tons of newsprint sent via de-inking.
  • Let “${\text{Bk}}_1$” be the tons of book paper sent via de-inking.
  • Let “${\text{Bx}}_2$” be the tons of boxboard sent via asphalt dispersion.
  • Let “${\text{Tis}}_2$”be the tons of tissue sent via asphalt dispersion.
  • Let “${\text{Ns}}_2$”be the tons of newsprint sent via asphalt dispersion.
  • Let “${\text{Bk}}_2$” be the tons of book paper sent via asphalt dispersion.
  • Let “Pb” be the available boxboard pulp.
  • Let “PTis” be the available tissue pulp.
  • Let “PNs” be the available newsprint pulp.
  • Let “PBk” be the available book paper pulp.
  • Let “${\text{PBx}}_{\text{j}}$” be the boxboard pulp utilized for grade “j” paper.
  • Let “${\text{PNs}}_{\text{j}}$”${\text{PTis}}_{\text{j}}$” be the tissue pulp utilized for grade “j” paper.
  • Let “${\text{PNs}}_{\text{j}}$” be the newsprint pulp utilized for grade “j” paper.
• The correct Linear Programming (LP) formulation is as follows,

  $\begin{array}{c}\text{min}\text{z=}5\text{Bx}+6\text{Tis}+8\text{Ns}+10\text{Bk}+20{\text{Bx}}_1+20{\text{Tis}}_1+20{\text{Ns}}_1+20{\text{Bk}}_1\\ +15{\text{Bx}}_2+15{\text{Tis}}_2+15{\text{Ns}}_2+15{\text{Bk}}_2\end{array}$

  $\begin{array}{l}\text{S}\end{array}$