DirectionsDirections: Read the given information carefully and answer the…
2024
Directions
Directions: Read the given information carefully and answer the question based on it: Four machines (A, B, C, and D) are arranged in a production line to manufacture a specific product. Each machine has distinct operational rules and performs a different function. The factory works from 9:00 AM to 5:00 PM every day, and each product must pass through the machines in a specific order to be completed. Each machine has a fixed processing time per product, and a machine cannot process more than one product at a time.
Information about the machines: Machine A takes 10 minutes to process a product; the products enter at 7-minute intervals starting at 9:00 AM. Machine B takes 15 minutes to process a product; it starts working only after Machine A has completed its task and sends the product forward. Machine C takes 20 minutes and requires a 5-minute cooldown before processing the next product. Machine D takes 12 minutes and can only start processing a product if it receives it before or exactly on the half-hour mark, otherwise the product waits until the next half-hour mark. The factory stops accepting new products at 4:00 PM.
At what time does the 6th product finish processing in Machine B?
Answer: E. None of these — ConceptThis is a single-server queueing problem. When items arrive at a station faster than the station can serve them, a queue forms: each item is served one…
- A.
9:45 AM
- B.
9:48 AM
- C.
9:50 AM
- D.
9:56 AM
- E.
None of these
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Show answer & explanation
Correct answer: E
Concept
This is a single-server queueing problem. When items arrive at a station faster than the station can serve them, a queue forms: each item is served one at a time, so an item starts only at max(its arrival time, the time the server becomes free), and finishes that start time plus the service time. The station with the longest service time becomes the bottleneck and ultimately sets the rhythm of departures.
Application
Work in minutes after 9:00 AM. The first six products enter Machine A at 0, 7, 14, 21, 28, 35 (i.e. 9:00, 9:07, 9:14, 9:21, 9:28, 9:35).
Machine A serves one product at a time and takes 10 minutes, but products arrive every 7 minutes (faster than 10), so a queue forms at A. Each product starts on A only when A is free:
Product 1: starts 0, finishes 10 (9:10).
Product 2: arrives 7, A free at 10, starts 10, finishes 20 (9:20).
Product 3: arrives 14, A free at 20, starts 20, finishes 30 (9:30).
Product 4: arrives 21, A free at 30, starts 30, finishes 40 (9:40).
Product 5: arrives 28, A free at 40, starts 40, finishes 50 (9:50).
Product 6: arrives 35, A free at 50, starts 50, finishes 60 (10:00).
Each product reaches Machine B exactly when it leaves A. Machine B serves one product at a time and takes 15 minutes, so the same queueing rule applies — B finishes a product at max(its A-finish, B's previous finish) + 15:
Product 1: arrives B at 10, B free, finishes 10+15 = 25 (9:25).
Product 2: arrives 20, B free at 25, finishes 25+15 = 40 (9:40).
Product 3: arrives 30, B free at 40, finishes 40+15 = 55 (9:55).
Product 4: arrives 40, B free at 55, finishes 55+15 = 70 (10:10).
Product 5: arrives 50, B free at 70, finishes 70+15 = 85 (10:25).
Product 6: arrives 60, B free at 85, finishes 85+15 = 100 (10:40).
So the 6th product finishes Machine B at 10:40 AM.
Cross-check
Once B is continuously busy, departures from B are spaced exactly 15 minutes apart: 9:25, 9:40, 9:55, 10:10, 10:25, 10:40 — confirming the 6th departure at 10:40 AM. The value 10:40 AM is not listed among 9:45, 9:48, 9:50 or 9:56, so the correct choice is "None of these".