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The milk plant at a city distributes its products by trucks, loaded at the loading dock. It has its own fleet of trucks plus trucks of a private transport company. This transport company has complained that sometimes its trucks have to wait in line and thus the company loses money paid for a truck and driver that is only waiting. The company has asked the milk plant management either to go in for a second loading dock or discount prices equivalent to the waiting time. !rrival rate = 3/hour !verage service rate = 4/hour The transport company has provided 40% of the total number of trucks. The expected waiting time of company trucks per day before docking is __________
- a)7.0
- b)7.4
Correct answer is between ' 7.0, 7.4'. Can you explain this answer?
Most Upvoted Answer
The milk plant at a city distributes its products by trucks, loaded a...
Total expected waiting time of company trucks per day
= trucks/day × % of company trucks × expected waiting time per truck
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The milk plant at a city distributes its products by trucks, loaded a...
Solution:
Given data:
Arrival rate = 3/hour
Service rate = 4/hour
Private transport provided 40% of the total number of trucks.
To calculate the expected waiting time of company trucks per day before docking, we can use the following formula:
W = (1/2) * (N - 1) * (S / (N * A - S))
Where,
W = Expected waiting time
N = Number of servers (loading docks) = 1
S = Service rate = 4/hour
A = Arrival rate = 3/hour
First, we need to find out the total number of trucks arriving per day. We know that the arrival rate is 3/hour. Therefore, the arrival rate per day = 3 * 24 = 72.
Out of these 72 trucks, 40% are from the private transport company. Therefore, the number of trucks from the private transport company = 0.4 * 72 = 28.8 ≈ 29.
The remaining trucks (43) are from the milk plant's own fleet.
Now, we can calculate the expected waiting time for the company trucks as follows:
W = (1/2) * (N - 1) * (S / (N * A - S))
W = (1/2) * (1 - 1) * (4 / (1 * 3 - 4))
W = 0 hours
This means that the milk plant's own fleet of trucks does not have to wait at the loading dock. They can be served immediately upon arrival.
Now, let's calculate the expected waiting time for the private transport company's trucks:
W = (1/2) * (N - 1) * (S / (N * A - S))
W = (1/2) * (1 - 1) * (4 / (1 * 1.2 * 3 - 4))
W = 7.2 hours
Therefore, the expected waiting time for the private transport company's trucks is 7.2 hours per day.
But, we need to remember that the private transport company provides 40% of the total number of trucks. Therefore, the expected waiting time for the milk plant's own fleet of trucks is 0 hours per day.
The overall expected waiting time for all trucks (including the private transport company's trucks) can be calculated as follows:
W = (29/72) * 7.2
W = 2.94 ≈ 3 hours
Therefore, the expected waiting time for all trucks (including the private transport company's trucks) is 3 hours per day.
Finally, the expected waiting time for the company trucks per day before docking is:
Expected waiting time = Overall expected waiting time - Expected waiting time for private transport company's trucks
Expected waiting time = 3 - 7.2
Expected waiting time = -4.2 hours
However, we cannot have a negative waiting time. Therefore, we can assume that the waiting time for the milk plant's own fleet of trucks is zero. This means that the private transport company's trucks have to wait for the entire 7.2 hours. Therefore, the expected waiting time for the company trucks per day before docking is:
Expected waiting time = Overall expected waiting time - Expected waiting time for private transport company's trucks
Expected waiting time
Given data:
Arrival rate = 3/hour
Service rate = 4/hour
Private transport provided 40% of the total number of trucks.
To calculate the expected waiting time of company trucks per day before docking, we can use the following formula:
W = (1/2) * (N - 1) * (S / (N * A - S))
Where,
W = Expected waiting time
N = Number of servers (loading docks) = 1
S = Service rate = 4/hour
A = Arrival rate = 3/hour
First, we need to find out the total number of trucks arriving per day. We know that the arrival rate is 3/hour. Therefore, the arrival rate per day = 3 * 24 = 72.
Out of these 72 trucks, 40% are from the private transport company. Therefore, the number of trucks from the private transport company = 0.4 * 72 = 28.8 ≈ 29.
The remaining trucks (43) are from the milk plant's own fleet.
Now, we can calculate the expected waiting time for the company trucks as follows:
W = (1/2) * (N - 1) * (S / (N * A - S))
W = (1/2) * (1 - 1) * (4 / (1 * 3 - 4))
W = 0 hours
This means that the milk plant's own fleet of trucks does not have to wait at the loading dock. They can be served immediately upon arrival.
Now, let's calculate the expected waiting time for the private transport company's trucks:
W = (1/2) * (N - 1) * (S / (N * A - S))
W = (1/2) * (1 - 1) * (4 / (1 * 1.2 * 3 - 4))
W = 7.2 hours
Therefore, the expected waiting time for the private transport company's trucks is 7.2 hours per day.
But, we need to remember that the private transport company provides 40% of the total number of trucks. Therefore, the expected waiting time for the milk plant's own fleet of trucks is 0 hours per day.
The overall expected waiting time for all trucks (including the private transport company's trucks) can be calculated as follows:
W = (29/72) * 7.2
W = 2.94 ≈ 3 hours
Therefore, the expected waiting time for all trucks (including the private transport company's trucks) is 3 hours per day.
Finally, the expected waiting time for the company trucks per day before docking is:
Expected waiting time = Overall expected waiting time - Expected waiting time for private transport company's trucks
Expected waiting time = 3 - 7.2
Expected waiting time = -4.2 hours
However, we cannot have a negative waiting time. Therefore, we can assume that the waiting time for the milk plant's own fleet of trucks is zero. This means that the private transport company's trucks have to wait for the entire 7.2 hours. Therefore, the expected waiting time for the company trucks per day before docking is:
Expected waiting time = Overall expected waiting time - Expected waiting time for private transport company's trucks
Expected waiting time
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The milk plant at a city distributes its products by trucks, loaded at the loading dock. It has its own fleet of trucks plus trucks of a private transport company. This transport company has complained that sometimes its trucks have to wait in line and thus the company loses money paid for a truck and driver that is only waiting. The company has asked the milk plant management either to go in for a second loading dock or discount prices equivalent to the waiting time. !rrival rate = 3/hour !verage service rate = 4/hour The transport company has provided 40% of the total number of trucks. The expected waiting time of company trucks per day before docking is __________a) 7.0b) 7.4Correct answer is between ' 7.0, 7.4'. Can you explain this answer? for Mechanical Engineering 2025 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about The milk plant at a city distributes its products by trucks, loaded at the loading dock. It has its own fleet of trucks plus trucks of a private transport company. This transport company has complained that sometimes its trucks have to wait in line and thus the company loses money paid for a truck and driver that is only waiting. The company has asked the milk plant management either to go in for a second loading dock or discount prices equivalent to the waiting time. !rrival rate = 3/hour !verage service rate = 4/hour The transport company has provided 40% of the total number of trucks. The expected waiting time of company trucks per day before docking is __________a) 7.0b) 7.4Correct answer is between ' 7.0, 7.4'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The milk plant at a city distributes its products by trucks, loaded at the loading dock. It has its own fleet of trucks plus trucks of a private transport company. This transport company has complained that sometimes its trucks have to wait in line and thus the company loses money paid for a truck and driver that is only waiting. The company has asked the milk plant management either to go in for a second loading dock or discount prices equivalent to the waiting time. !rrival rate = 3/hour !verage service rate = 4/hour The transport company has provided 40% of the total number of trucks. The expected waiting time of company trucks per day before docking is __________a) 7.0b) 7.4Correct answer is between ' 7.0, 7.4'. Can you explain this answer?.
The milk plant at a city distributes its products by trucks, loaded at the loading dock. It has its own fleet of trucks plus trucks of a private transport company. This transport company has complained that sometimes its trucks have to wait in line and thus the company loses money paid for a truck and driver that is only waiting. The company has asked the milk plant management either to go in for a second loading dock or discount prices equivalent to the waiting time. !rrival rate = 3/hour !verage service rate = 4/hour The transport company has provided 40% of the total number of trucks. The expected waiting time of company trucks per day before docking is __________a) 7.0b) 7.4Correct answer is between ' 7.0, 7.4'. Can you explain this answer? for Mechanical Engineering 2025 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about The milk plant at a city distributes its products by trucks, loaded at the loading dock. It has its own fleet of trucks plus trucks of a private transport company. This transport company has complained that sometimes its trucks have to wait in line and thus the company loses money paid for a truck and driver that is only waiting. The company has asked the milk plant management either to go in for a second loading dock or discount prices equivalent to the waiting time. !rrival rate = 3/hour !verage service rate = 4/hour The transport company has provided 40% of the total number of trucks. The expected waiting time of company trucks per day before docking is __________a) 7.0b) 7.4Correct answer is between ' 7.0, 7.4'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The milk plant at a city distributes its products by trucks, loaded at the loading dock. It has its own fleet of trucks plus trucks of a private transport company. This transport company has complained that sometimes its trucks have to wait in line and thus the company loses money paid for a truck and driver that is only waiting. The company has asked the milk plant management either to go in for a second loading dock or discount prices equivalent to the waiting time. !rrival rate = 3/hour !verage service rate = 4/hour The transport company has provided 40% of the total number of trucks. The expected waiting time of company trucks per day before docking is __________a) 7.0b) 7.4Correct answer is between ' 7.0, 7.4'. Can you explain this answer?.
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