Chapter 3.10, Problem 5P

Explanation of Solution

Formulation of Linear Programming (LP):

• Assume the following,
  • Let “${\text{T}}_{\text{m}}$” be the trucks made during the month “m”.
  • “${\text{C}}_{\text{m}}$” be the trucks made during the month “m”.
  • “${\text{S}}_{\text{m}}$” be the number of steel bought during the month “m”.
  • “${\text{CI}}_{\text{m}}$” be the demands for cars in inventory at the end of the month “m”.
  • “${\text{TI}}_{\text{m}}$” be the demands for trucks in inventory at the end of the month “m”.
• The Linear Programming (LP) is formulated as follows,

${\text{mincost=400S}}_{\text{1}}{\text{+600S}}_2{\text{+150(TI}}_{\text{1}}{\text{+CI}}_{\text{1}}+{\text{TI}}_2+{\text{CI}}_2)$

such that,

• All variables >= “0”.
• “${\text{TI}}_{\text{1}}{\text{ = 100 + T}}_{\text{1}}-\text{400 }$” that denotes the demands for the trucks in inventory at the end of the month “1”.
• “${\text{TI}}_2{\text{ = TI}}_1{\text{+ T}}_2-3\text{00 }$”that denotes the demands for the trucks in inventory at the end of the month “2”.
• “${\text{CI}}_1=200+{\text{C}}_{\text{1}}-800$” that denotes the demands for the trucks in inventory at the end of the month “1”