Chapter 3.10, Problem 4P

Explanation of Solution

Determination of production schedule to minimize the cost:

• Assume the following,
  • Let “${\text{A}}_{\text{xy}}$” be the product A’s units produced during the month “x” on line “y”.
  • Let “${\text{B}}_{\text{xy}}$” be the product B’s units produced during the month “x” on line “y”.
  • Let “${\text{IA}}_{\text{m}}$” be the product A’s units in inventory at the end of the month “m”.
  • Let “${\text{IB}}_{\text{m}}$” be the product B’s units in inventory at the end of the month “m”.
• Consider “$\text{x=1}$” as March, and “$\text{x=2}$” as April.
• The Linear Programming (LP) is formulated as follows,

$\text{mincost=0}{\text{.75A}}_{\text{21}}\text{+0}{\text{.75A}}_{\text{11}}\text{+0}{\text{.80A}}_{\text{12}}\text{+0}{\text{.80A}}_{\text{22}}\text{+0}{\text{.60B}}_{\text{11}}\text{+ 0}{\text{.60B}}_{\text{21}}\text{+0}{\text{.70B}}_{\text{12}}\text{+0}{\text{.70B}}_{\text{22}}\text{+0}{\text{.20IA}}_{\text{1}}\text{+0}{\text{.20IA}}_2\text{+0}{\text{.20IB}}_{\text{1}}+\text{0}{}_{}$