Chapter 3.10, Problem 6P

Explanation of Solution

Formulation of Linear Programming (LP):

• Assume the following,
  • Let “${\text{S}}_{\text{m}}$” be the shirts made in the month “m” at regular time.
  • “${\text{S}}_{\text{m}}\text{'}$” be the shirts made in the month “m” at overtime.
  • “${\text{P}}_{\text{m}}$” be the pants made in the month “m” at regular time.
  • “${\text{P}}_{\text{m}}\text{'}$” be the pans made in the month “m” at overtime.
  • “${\text{SI}}_{\text{m}}$” be the demands for shirts in inventory at the end of the month “m”.
  • “${\text{PI}}_{\text{m}}$” be the demands for pants in inventory at the end of the month “m”.
• The Linear Programming (LP) is formulated as follows,

${\text{min z=4(S}}_{\text{1}}{\text{+P}}_{\text{1}}{\text{+S}}_{\text{2}}{\text{+P}}_{\text{2}}{\text{)+8(S}}_{\text{1}}{\text{'+P}}_{\text{1}}{\text{'+S}}_{\text{2}}{\text{'+P}}_{\text{2}}{\text{')+3(SI}}_{\text{1}}{\text{+PI}}_{\text{1}}{\text{+SI}}_{\text{2}}{\text{+PI}}_{\text{2}}\text{)}$

such that,

• All variables >= “0”.
• “${\text{SI}}_{\text{1}}{\text{ = 1+S}}_{\text{1}}{\text{+S}}_{\text{1}}\text{'}-1\text{0 }$” that denotes the demands for the shirts in inventory at the end of the month “1”.
• “${\text{SI}}_2{\text{ = SI}}_1{\text{+S}}_2{\text{+S}}_2\text{'}-12$” that denotes the demands for the shirts in inventory at the end of the month “2”