A retail company has 720 sales representatives. Each first‑level manager can effectively supervise at most 15 sales representatives. (a) Find the minimum number of first‑level managers required. (b) If the company wants a two‑level managerial hierarchy (first‑level and second‑level managers) with the same span of control of 15, how many second‑level managers are needed to supervise the first‑level managers? Assume no manager supervises themselves.
Answer
(a) 48 first‑level managers; (b) 4 second‑level managers.
The correct answer is (a) 48 first‑level managers; (b) 4 second‑level managers. — State the results for part (a) and part (b).
Step-by-step solution
- Compute the number of first‑level managers needed: divide total reps by span of control and round up: 720 ÷ 15 = 48 exactly, so 48 managers are required.
- These 48 first‑level managers now become the subordinates for the second level.
- Apply the same span of control (15) to the second level: divide 48 by 15 and round up: 48 ÷ 15 = 3.2, round up to 4.
- Thus, 4 second‑level managers are needed to supervise the 48 first‑level managers.
- State the results for part (a) and part (b).
Common mistake: Failing to round up when the division does not give a whole number, leading to an underestimate of managers required.
Concept tested: Span of control and managerial hierarchy
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