Chapter 3, Problem 50RP

Explanation of Solution

LP to minimize the total cost of disposing waste:

• Assume the following,
  • Let “${\text{W}}_{\text{mn}}$” be the tons of city “m” waste, which is incinerated at incinerator “n”.
  • Let “${\text{D}}_{\text{mn}}$” be the tons of debris received by landfill “n” from incinerator “m”.
• The Linear Programming (LP) to minimize the total cost of disposing waste of both cities is as follows,

$\begin{array}{c}\text{Min}{\text{z=40(W}}_{\text{11}}{\text{+W}}_{\text{21}}\text{)+30}\left({\text{W}}_{\text{12}}{\text{+W}}_{\text{22}}\right){\text{+3[30W}}_{\text{11}}{\text{+5W}}_{\text{12}}{\text{+36W}}_{\text{21}}{\text{+42W}}_{\text{22}}\\ {\text{+5D}}_{\text{11}}{\text{+8D}}_{\text{12}}{\text{+9D}}_{\text{21}}{\text{+6D}}_{\text{22}}\text{]}\end{array}$

• The above function subject to the following conditions,
  • “${\text{W}}_{\text{11}}{\text{+W}}_{\text{12}}=500$” represents tons of waste produced by city “1” for a day.
  • “${\text{W}}_{\text{21}}{\text{+W}}_{\text{22}}=400$” represents tons of waste produced by city “2” for a day