At Arihant Prakashan, every book goes through three stages: typing, composing and binding. There are 16 typists, 10 composers and 15 binders. A typist can type 8 books per hour, a composer can compose 12 books per hour, and a binder can bind 12 books per hour. All workers work 10 hours per day, and each person performs only their own type of job. What is the maximum number of complete books that can be prepared in one day?

Introduction / Context:
This production planning question focuses on identifying the bottleneck stage in a multi step workflow. Books at a publishing house go through typing, composing and binding. Each stage has a certain capacity, and the lowest stage capacity determines the overall daily output of complete books.

Given Data / Assumptions:
• Typing stage: 16 typists, each can type 8 books per hour.
• Composing stage: 10 composers, each can compose 12 books per hour.
• Binding stage: 15 binders, each can bind 12 books per hour.
• Every person works 10 hours per day.
• A book must pass all three stages to be counted as complete.

Concept / Approach:
We first compute the hourly capacity of each stage by multiplying the number of workers by their individual rates. Multiplying by 10 hours gives each stage daily capacity. The daily number of completed books cannot exceed the smallest of these capacities, because the slowest stage limits the throughput of the entire process.

Step-by-Step Solution:
Step 1: Calculate hourly capacity for typing. Typing capacity per hour = 16 typists × 8 books per hour = 128 books per hour. Daily typing capacity = 128 × 10 = 1280 books per day. Step 2: Calculate hourly capacity for composing. Composing capacity per hour = 10 composers × 12 books per hour = 120 books per hour. Daily composing capacity = 120 × 10 = 1200 books per day. Step 3: Calculate hourly capacity for binding. Binding capacity per hour = 15 binders × 12 books per hour = 180 books per hour. Daily binding capacity = 180 × 10 = 1800 books per day. Step 4: The overall daily output is limited by the smallest stage capacity. Minimum daily capacity = min(1280, 1200, 1800) = 1200 books per day.

Verification / Alternative check:
We can see that even if the typists could type 1280 books and binders could bind 1800 books, only 1200 books can be composed. Without completion of composing, books cannot proceed to the binding stage. Therefore, the composing stage is the bottleneck and determines the total number of complete books.

Why Other Options Are Wrong:
Values above 1200, such as 1380, 1440 or 1500, exceed the composing capacity and therefore are not feasible. The process simply cannot produce more composed books, hence cannot produce more finished books than 1200 per day. Only 1200 respects the bottleneck limitation.

Common Pitfalls:
A common mistake is to sum capacities of all stages or choose the highest capacity instead of the lowest. Another error is to overlook the working hours per day, leading to incorrect computation of daily capacity. Always identify the slowest stage in a sequence of dependent tasks.

Final Answer:
A maximum of 1200 complete books can be prepared in one day.