Chapter 3, Problem 46RP

Explanation of Solution

LP to achieve the teller requirements:

• Assume the following,
  • Let “${\text{FT}}_{\text{12}}$” be the full-time workers who go for the lunch between “12” to “1”.
  • Let “${\text{FT}}_{\text{1}}$”be the full-time workers who go for “1” to “2” lunch.
  • Let “${\text{P}}_{\text{T}}$” be the part-time workers who start work at time “T” and “T” belongs to the values “9”, “10”, “11”, “12”, “1”, and “2”.
• An appropriate Linear Programming (LP) is given as follows,

${\text{Min z=64(FT}}_{\text{12}}+{\text{FT}}_1)+15({\text{P}}_9+{\text{P}}_{10}+{\text{P}}_{11}+{\text{P}}_{12}+{\text{P}}_1+{\text{P}}_2)$

• The above function subject to the following conditions,
  • “${\text{FT}}_{12}+{\text{FT}}_1+{\text{P}}_9\ge 4$” denotes that the number of workers required for the time period “9-10” should be “4”.
  • “${\text{FT}}_{12}+{\text{FT}}_1+{\text{P}}_9+{\text{P}}_{10}\ge 3$”denotes that the number of workers required for the time period “10-11” should be “3”.
  • “${\text{FT}}_{12}+{\text{FT}}_1+{\text{P}}_9+{\text{P}}_{10}+{\text{P}}_{11}\ge 4$”denotes that the number of workers required for the time period “11” to “12” should be “4”

Explanation of Solution

Employment policy:

• The variables are limited to be integers.
• If so, the best solution is to set the full-time employees who work at “12” to “1” lunch and “1” to “2” lunch as “3”...