Question

Operations Management - First session Case Your boss has tasked you with following assignment You must assign offices to six staff members (there are eight staff members, but some of them may not be entitled to an office). The available offices, numbered 1- 6 consecutively, are arranged in a row, and are separated only by dividers. Therefore, sounds, and cigarettes smoke readily pass from each office to those on either side. • Neeta's work requires her to speak on the telephone frequently throughout the day. • Komal and Jasleen often talk to one another in their work, and prefer to have adjacent offices. Amit, the senior employee, is entitled to Office 5, which has the largest window. Deepti needs silence in the office(s) adjacent to her own. Ahmad, Lucky, and Deepankar all smoke. Amit is allergic to tobacco smoke and must have non-smokers in the office(s) adjacent to his own. • Unless otherwise specified, all employees maintain silence while in their offices We wish to know how many total assignments (configurations) are possible. Please provide this number. It is important to know this number since similar assignments can be made on the basis of other requests and also at different office locations. Following are some questions that the manager has asked you. 1) The best location for Komal is in Office ? - 3 2) The best employee to occupy the office furthest from Jasleen would be ? 3) The three employees who smoke can only be placed in Offices? Deepti a be? - Deepts-sila tal 4 How many arrangements are possible ? 12 and 3 Med Amit

Answer 1

Solution:

8 people / 6 available rooms

1         2           3          4          5          6

                                              Amit

Given -

Location of Amit has been fixed at 5th

Smoke and Sound pass to rooms on either side

Neeta has got Phone

Komal Jasleen always adjacent to together

Deepti needs clear silence, no people with phone adjacent,So Neeta, Deepti can never be adjacent

Ahmed Lucky Dipankar smokes, as per the given conditions, they can't sit beside Amit, and can only take 1,2,3 rooms

All possible conditions-

(Ahmed/Lucky/Dipankar) (Komal/Jasleen) (Deepti/Neeta) Amit (Neeta/Deepti) – 3*2!*2!*2! - 24 choices

1 Room 2 Rooms 1 Room Amit 1 Room

(Ahmed/Lucky/Dipankar) (Deepti/Neeta) Amit (Neeta/Deepti) - 3!*2! - 12 choices

3 Rooms 1 Room Amit 1 Room

1. Best Location for Komal in the office is 2nd or 3rd Room

2. The best employee to occupy space furthest from Jasleen would be either Neeta or Deepti

3. The 3 employees who smoke can only be placed in Room 1,2 or 3  

4. Total Number of arrangements possible - 24 + 12 = 36