A manufacturing firm has 300 production line workers. The plant manager decides that each production supervisor can supervise at most 20 workers. (a) What is the minimum number of production supervisors required? (b) If the plant also wants a second level of supervision (first‑level supervisors and second‑level managers) with the same span of control 20, how many second‑level managers are needed to supervise the first‑level supervisors?

Step-by-step solution

1. Step 1: Divide the total workers by the span of control: $\frac{300}{20}=15$. Reason: This gives the exact number of supervisors needed.
2. Step 2: Since we cannot have a fraction of a supervisor, use the ceiling function: $\lceil 15\rceil =15$.
3. Step 3: To find second‑level managers, divide the 15 supervisors by the same span: $\frac{15}{20}=0.75$.
4. Step 4: Apply ceiling again: $\lceil 0.75\rceil =1$.
5. Step 5: Conclude that 15 first‑level supervisors and 1 second‑level manager are required.

Concept tested: Span of control and hierarchical structure

Published 13 October 2026 · How this solution was prepared and checked