Chapter 3, Problem 19RP

Explanation of Solution

Linear Programming (LP) to minimize the weekly cost:

• Assume the following,
  • Let “${\text{g}}_{\text{1}}$” be the cubic foot of grade “1” lumber purchased.
  • Let “${\text{g}}_2$” be the cubic foot of grade “1” lumber purchased.
  • Let “L” be the cubit foot of logs cut.
• The LP to minimize the weekly cost of meeting the demand for processed lumber is as follows,

  ${\text{min z = 3g}}_{\text{1}}{\text{+7g}}_{\text{2}}\text{+3L+2}{\text{.5L+4(g}}_{\text{1}}{\text{+g}}_{\text{2}}\text{+L)}$

• The above function subject to the following constraints,
  • “${\text{g}}_1\le \text{40000}$” denotes that the maximum of “40000” cubic foot of grade “1” lumber can be bought