A librarian at a college library on an average could process

A librarian at a college library, on an average, could process 18 students during one hour. On an average, a student arrives to her at every 4 minutes. Assume it is a single-server waiting line model. Now suppose the librarian can be replaced by a specialist, who must be paid $32 per hour whereas the current librarian is paid $22 per hour. The specialist can process 22 students in one hour. If a student\'s time is considered to be worth $10 per hour, is it worth to replace the current librarian with the specialist?

Solution

Assuming A Students comes at every 4 min;

means in an hour 15 students comes to her;

That means 15 students are comming at counter every hour;

lets calculate hourly cost;

Librarian = $22 + 15 students /hour * (60/18 minute on each student) * $10 /60 per student;

= 22+ 15* 10 /18;

22+25/3 = $30.333; is the cost because of librarian;

Specialist = 32 + 15 students /hour * (60/22 minute on each student) * $10 /60 per student;

Specialist = 32 + 75/11 = $38.82;

so librarian is still a better choice;