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CMA Foundation · Fundamentals of Business Economics and Management · Planning, Organizing, Staffing and Leading

The graduate-level concept of Graicunas relates the number of possible relationships to subordinates, and the usual formula for total relationships is n[2^(n-1) + (n-1)]. For a manager with 3 subordinates, the total number of relationships is:

The total is 18 relationships. Using Graicunas's formula n[2^(n-1) + (n-1)] with n = 3 gives 3 × (4 + 2) = 3 × 6 = 18. This covers direct single, direct group and cross relationships, showing how quickly complexity grows as subordinates are added.

  1. A9
  2. B12
  3. C18Correct
  4. D25

Explanation

Substitute n = 3: 2^(3-1) = 4, and n-1 = 2, so the bracket is 4 + 2 = 6. Multiply by n: 3 × 6 = 18. The value 9 comes from computing 3 × 3 only, ignoring the exponent term, and 12 results from forgetting to add (n-1) and using 3 × 4.

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