Chapter 3.5, Problem 4P

Explanation of Solution

Formulation of LP:

Let,

${\text{x}}_{\text{1}}$= Number of full-time employees required on Monday is 17.

${\text{x}}_2$= Number of full-time employees required on Tuesday is 13.

${\text{x}}_3$= Number of full-time employees required on Wednesday is 15.

${\text{x}}_4$= Number of full-time employees required on Thursday is 19.

${\text{x}}_5$= Number of full-time employees required on Friday is 14.

${\text{x}}_6$= Number of full-time employees required on Saturday is 16.

${\text{x}}_7$= Number of full-time employees required on Sunday is 11.

The objective is to schedule the employees in order to maximize the number of weekend days off received by the employees.

Then the LP is becomes,

Maximize, $z=x_7+2x_1+x_2$

$\begin{array}{l}{\displaystyle \sum _{\text{i}}{\text{x}}_{\text{i}}{\text{-x}}_{\text{2}}{\text{-x}}_{\text{3}}\ge \text{17}}\\ {\displaystyle \sum _{\text{i}}{\text{x}}_{\text{i}}{\text{-x}}_3{\text{-x}}_4\ge \text{13}}\\ \end{array}$