Suppose the post office had 25 fulltime employees and was no

Suppose the post office had 25 full-time employees and was not allowed to hire or fire any employees. Formulate an LP that could be used to schedule the employees in order to maximize the number of weekend days off received by the employees.

Solution

we have to maximize the number of weekend days off received by the employees.

In other words minimize the number of work days by the employees.

Let x1 be the number of people start working on Monday.
Let x2 be the number of people start working on Tuesday.
Let x3 be the number of people start working on Wedday.
Let x4 be the number of people start working on thursday.
Let x5 be the number of people start working on Friday.
Let x6 be the number of people start working on Saturday.
Let x7 be the number of people start working on sunday.

Let\'s assume that working are 5 in a week.
Then formulation of LPP problem is given by
Min Z= x7 +2x1 +x2
subject to constraints:
x1+x4+x5+x6+x7>=17
x1+x2+x5+x6+x7>=13
x1+x2+x3+x6+x7>=15
x1+x2+x3+x4+x7>=19
x1+x2+x3+x4+x5>=14
x2+x3+x4+x5+x6>=16
x3+x4+x5+x6+x7>=11
x1+x2+x3+x4+x5+x6+x7=25
x1,x2,x3,x4,x5,x6,x7>=0