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On an average 96 patients per 24-hours day require the service of an emergency clinic. Also on the average a patient requires 10 minute of active attention. Assume that the facility can handle only one emergency at a time suppose that it costs the clinic Rs.100 per patient treated to obtain an average servicing time of 10 minute, and that each minute of decrease in this average time would cost the clinic Rs.10 per patient treated. How much would have to be budgeted by the clinic to decrease the average size of the queue from
1
1
3
patients to 1/2 patients.
(A)123
(B)127
Correct answer is between ','. Can you explain this answer?
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Verified Answer
On an average 96 patients per 24-hours day require the service of an ...
μ = 1/10 × 60 = 6/hour
This number is to be reduced from
μ′ = 8, −4
μ′ = 8
Average time required by each patient
required to attend a patient
∴ budget required for each patient
Most Upvoted Answer
On an average 96 patients per 24-hours day require the service of an ...
Given data:
- Average number of patients per 24-hours day = 96
- Time required for each patient = 10 minutes
- Facility can handle only one emergency at a time
- Cost to clinic for treating one patient in 10 minutes = Rs. 100
- Cost increase to clinic for decreasing average servicing time by 1 minute = Rs. 10
- Average queue size to be decreased from 113 patients to 1/2 patients
Calculations:
1. Average time spent by each patient in queue:
- Total time available in 24 hours = 24*60 = 1440 minutes
- Time spent by one patient = 10 minutes
- Number of patients in 24 hours = 96
- Total time spent by all patients = 96*10 = 960 minutes
- Time spent by patients in queue = Total time available - Total time spent by patients = 1440 - 960 = 480 minutes
- Average time spent by each patient in queue = Time spent by patients in queue / Number of patients = 480/96 = 5 minutes
2. Cost to clinic for decreasing average servicing time:
- Assuming that the clinic is currently servicing patients at an average time of 5+10=15 minutes (5 minutes in queue + 10 minutes of active attention)
- Cost of treating one patient at 15 minutes = Rs. 100
- To decrease the average servicing time by 1 minute, the cost will increase by Rs. 10 per patient
- Therefore, to decrease the average servicing time from 15 minutes to 14 minutes, the cost will increase by Rs. 10*96 = Rs. 960
- To decrease the average servicing time from 15 minutes to 5 minutes (assuming no queue time), the cost will increase by Rs. 10*960 = Rs. 9600
3. Budget required to decrease the queue size:
- Assuming that the queue size is reduced by x patients (i.e. from 113 to 1/2), then the total time spent by patients in queue will be reduced by 5x minutes
- Therefore, the average servicing time can be decreased by 5x minutes without increasing the total time spent by patients
- To decrease the average servicing time by 5x minutes, the cost will increase by Rs. 10*96*x = Rs. 960x
- Equating the cost increase to the budget required, we get:
960x = Budget
- Substituting x = 113/2 - 1/2 = 56, we get:
Budget = 960*56 = Rs. 53760
Answer: The budget required by the clinic to decrease the average size of the queue from 113 patients to 1/2 patients is Rs. 53760, which is option (B).
- Average number of patients per 24-hours day = 96
- Time required for each patient = 10 minutes
- Facility can handle only one emergency at a time
- Cost to clinic for treating one patient in 10 minutes = Rs. 100
- Cost increase to clinic for decreasing average servicing time by 1 minute = Rs. 10
- Average queue size to be decreased from 113 patients to 1/2 patients
Calculations:
1. Average time spent by each patient in queue:
- Total time available in 24 hours = 24*60 = 1440 minutes
- Time spent by one patient = 10 minutes
- Number of patients in 24 hours = 96
- Total time spent by all patients = 96*10 = 960 minutes
- Time spent by patients in queue = Total time available - Total time spent by patients = 1440 - 960 = 480 minutes
- Average time spent by each patient in queue = Time spent by patients in queue / Number of patients = 480/96 = 5 minutes
2. Cost to clinic for decreasing average servicing time:
- Assuming that the clinic is currently servicing patients at an average time of 5+10=15 minutes (5 minutes in queue + 10 minutes of active attention)
- Cost of treating one patient at 15 minutes = Rs. 100
- To decrease the average servicing time by 1 minute, the cost will increase by Rs. 10 per patient
- Therefore, to decrease the average servicing time from 15 minutes to 14 minutes, the cost will increase by Rs. 10*96 = Rs. 960
- To decrease the average servicing time from 15 minutes to 5 minutes (assuming no queue time), the cost will increase by Rs. 10*960 = Rs. 9600
3. Budget required to decrease the queue size:
- Assuming that the queue size is reduced by x patients (i.e. from 113 to 1/2), then the total time spent by patients in queue will be reduced by 5x minutes
- Therefore, the average servicing time can be decreased by 5x minutes without increasing the total time spent by patients
- To decrease the average servicing time by 5x minutes, the cost will increase by Rs. 10*96*x = Rs. 960x
- Equating the cost increase to the budget required, we get:
960x = Budget
- Substituting x = 113/2 - 1/2 = 56, we get:
Budget = 960*56 = Rs. 53760
Answer: The budget required by the clinic to decrease the average size of the queue from 113 patients to 1/2 patients is Rs. 53760, which is option (B).
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On an average 96 patients per 24-hours day require the service of an emergency clinic. Also on the average a patient requires 10 minute of active attention. Assume that the facility can handle only one emergency at a time suppose that it costs the clinic Rs.100 per patient treated to obtain an average servicing time of 10 minute, and that each minute of decrease in this average time would cost the clinic Rs.10 per patient treated. How much would have to be budgeted by the clinic to decrease the average size of the queue from113patients to 1/2 patients.(A)123(B)127Correct answer is between ','. Can you explain this answer?
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On an average 96 patients per 24-hours day require the service of an emergency clinic. Also on the average a patient requires 10 minute of active attention. Assume that the facility can handle only one emergency at a time suppose that it costs the clinic Rs.100 per patient treated to obtain an average servicing time of 10 minute, and that each minute of decrease in this average time would cost the clinic Rs.10 per patient treated. How much would have to be budgeted by the clinic to decrease the average size of the queue from113patients to 1/2 patients.(A)123(B)127Correct answer is between ','. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about On an average 96 patients per 24-hours day require the service of an emergency clinic. Also on the average a patient requires 10 minute of active attention. Assume that the facility can handle only one emergency at a time suppose that it costs the clinic Rs.100 per patient treated to obtain an average servicing time of 10 minute, and that each minute of decrease in this average time would cost the clinic Rs.10 per patient treated. How much would have to be budgeted by the clinic to decrease the average size of the queue from113patients to 1/2 patients.(A)123(B)127Correct answer is between ','. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for On an average 96 patients per 24-hours day require the service of an emergency clinic. Also on the average a patient requires 10 minute of active attention. Assume that the facility can handle only one emergency at a time suppose that it costs the clinic Rs.100 per patient treated to obtain an average servicing time of 10 minute, and that each minute of decrease in this average time would cost the clinic Rs.10 per patient treated. How much would have to be budgeted by the clinic to decrease the average size of the queue from113patients to 1/2 patients.(A)123(B)127Correct answer is between ','. Can you explain this answer?.
On an average 96 patients per 24-hours day require the service of an emergency clinic. Also on the average a patient requires 10 minute of active attention. Assume that the facility can handle only one emergency at a time suppose that it costs the clinic Rs.100 per patient treated to obtain an average servicing time of 10 minute, and that each minute of decrease in this average time would cost the clinic Rs.10 per patient treated. How much would have to be budgeted by the clinic to decrease the average size of the queue from113patients to 1/2 patients.(A)123(B)127Correct answer is between ','. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about On an average 96 patients per 24-hours day require the service of an emergency clinic. Also on the average a patient requires 10 minute of active attention. Assume that the facility can handle only one emergency at a time suppose that it costs the clinic Rs.100 per patient treated to obtain an average servicing time of 10 minute, and that each minute of decrease in this average time would cost the clinic Rs.10 per patient treated. How much would have to be budgeted by the clinic to decrease the average size of the queue from113patients to 1/2 patients.(A)123(B)127Correct answer is between ','. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for On an average 96 patients per 24-hours day require the service of an emergency clinic. Also on the average a patient requires 10 minute of active attention. Assume that the facility can handle only one emergency at a time suppose that it costs the clinic Rs.100 per patient treated to obtain an average servicing time of 10 minute, and that each minute of decrease in this average time would cost the clinic Rs.10 per patient treated. How much would have to be budgeted by the clinic to decrease the average size of the queue from113patients to 1/2 patients.(A)123(B)127Correct answer is between ','. Can you explain this answer?.
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