Chapter 3.10, Problem 7P

Explanation of Solution

Formulation of Linear Programming (LP):

• Assume the following,
  • Let “${\text{S}}_{\text{m}}$” be the pair of shoes produced during the quarter “m” of each year.
  • “${\text{SI}}_{\text{m}}$” be the demands for the pair of shoes in inventory at the end of each year.
  • “${\text{W}}_{\text{m}}$” be the workers getting quarter “m” off during each year.
• The Linear Programming (LP) is formulated to minimize the cost per year as follows,

${\text{min z=1500(W}}_{\text{1}}{\text{+W}}_2{\text{+W}}_3{\text{+W}}_4{\text{)+50SI}}_{\text{1}}{\text{+50SI}}_2{\text{+50SI}}_3{\text{+50SI}}_4$

such that,

• All variables >= “0”.
• “${\text{SI}}_{\text{1}}{\text{ = 0+S}}_{\text{1}}-60\text{0 }$” that denotes the demands for the pair of shoes in inventory at the end of each year.
• “${\text{SI}}_2{\text{ = SI}}_{\text{1}}+{\text{S}}_2-30\text{0 }$” that denotes the demands for the pair of shoes in inventory at the end of each year.
• “${\text{SI}}_3{\text{ = SI}}_2+{\text{S}}_3-80\text{0 }$” that denotes the demands for the pair of shoes in inventory at the end of each year