Chapter 3, Problem 44RP

Explanation of Solution

Maximizing refinery’s profit:

• Assume the following,
  • Let “${\text{BM}}_{\text{j}}$” be the barrels operated by method “j”.
  • Let “$\text{BG6C}$” be the barrel of grade “6” cracked.
  • Let “$\text{BG8C}$” be the barrel of grade “8” cracked.
  • Let “$\text{BG6}$” be the barrel of grade “6” not cracked further.
  • Let “$\text{BG8}$” be the barrel of grade “8” not cracked further.
  • Let “$\text{BG}$” be the barrels of gas manufactured.
  • Let “$\text{BHO}$” be the barrels of heating oil manufactured.
  • Let “$\text{BG6G}$” be the barrel of grade “6” used to make a gas.
  • Let “$\text{BG8G}$” be the barrel of grade “6” used to make a gas.
  • Let “$\text{BG10G}$” be the barrel of grade “6” used to make a gas.
  • Let “$\text{BG6H}$” be the barrel of grade “6” used to manufacture heating oil.
  • Let “$\text{BG8H}$” be the barrel of grade “6” used to manufacture heating oil.
  • Let “$\text{BG10H}$” be the barrel of grade “6” used to manufacture heating oil.
• The objective function to maximize the profit of refinery is as follows,

$\text{Max z=11BG+6BHO}-\text{3}{\text{.4BM}}_{\text{1}}-{\text{3BM}}_{\text{2}}-\text{2}{\text{.6BM}}_{\text{3}}-\text{BG6C}-\text{1}\text{.5BG8C}$

• The above function subject to the following conditions,
  • “$\text{BG6C+BG6=0}{}_{}$