What Are Functional Levels Of Management?

The total number of employees in an organization is 729. The management decided to divide the organizational hierarchy into levels so that each supervisor controls 3 persons. How many levels will be created and how many supervisors will be required at each level of the organization?

• A) 7 levels, 364 supervisors B) 6 levels, 364 supervisors C) 6 levels, 243 supervisors D) 7 levels, 363 supervisors

• Answer:

  Since every supervisor can take 3 subordinates, lets assume the bottom level workers to be 'x' (level 1) Level 1 Workers: X Level 2 Supervisors: X/3 Level 3 Supervisors: X/3^2 = X/9 and so on... Level 7 Supervisors: X/3^6 = X/729 which is clearly zero since sum of all workers in organization is 729 (including workers at all levels). So there cannot be 7 levels. Assuming 6 levels, total number of workers (in terms of X) = X + X/3 + X/9 + X/27 + ..... + X/243 ...... Looks like Option (C) is correct, but lets solve it anyway. = X(1 + 1/3 + 1/9 + ... 1/243) which is a finite Geometric Progression = X(1- 1/729) /(1-1/3).... Lets assume 1/729 ~0 = 3X/2 Since total strength of the organization is 729, 3X/2 = 729 => X = 486 workers Since 486 workers are in Level 1, the remaining 243 are supervisors from levels 2 to 6.