Chapter 3.5, Problem 3P

Explanation of Solution

Formulation of LP:

Let,

$x_1$= Number of employees who start work on Sunday and work 5 days.

$x_2$= Number of employees who start work on Monday and work 5 days.

$x_3$= Number of employees who start work on Tuesday and work 5 days.

$x_4$= Number of employees who start work on Wednesday and work 5 days.

$x_5$= Number of employees who start work on Thursday and work 5 days.

$x_6$= Number of employees who start work on Friday and work 5 days.

$x_7$= Number of employees who start work on Saturday and work 5 days.

$y_1$= Number of employees who start work on Sunday and work 5 days.

$y_2$= Number of employees who start work on Monday and work 5 days.

$y_3$= Number of employees who start work on Tuesday and work 5 days.

$y_4$= Number of employees who start work on Wednesday and work 5 days.

$y_5$= Number of employees who start work on Thursday and work 5 days.

$y_6$= Number of employees who start work on Friday and work 5 days.

$y_7$= Number of employees who start work on Saturday and work 5 days.

Then the appropriate LP is given below,

Minimize, $z= 250\left(x_1+x_2+x_3+x_4+x_5+x_6+x_7\right)+312\left(y_1+y_2+y_3+y_4+y_6+y_7\right)$

Subject to the constraints,

${\text{x}}_{\text{1}}{\text{+x}}_{\text{4}}{\text{+x}}_{\text{5}}{\text{+x}}_{\text{6}}{\text{+x}}_{\text{7}}{\text{+y}}_{\text{1}}{\text{+y}}_{\text{3}}{\text{+y}}_{\text{4}}{\text{+y}}_{\text{5}}{\text{+y}}_{\text{6}}{\text{+y}}_{\text{7}}\ge \text{11 }\left(\text{Sunday}\right)$

${\text{x}}_{\text{1}}{\text{+x}}_{\text{2}}{\text{+x}}_{\text{5}}{\text{+x}}_{}$