value 10.00 points Problem 18-1 Repair calls are handled by one repairman at a p
ID: 422584 • Letter: V
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value 10.00 points Problem 18-1 Repair calls are handled by one repairman at a photocopy shop. Repair time, including travel time, is exponentially distributed, with a mean of 2.5 hours per call Requests for copier repairs come in at a mean rate of 2.1 per eight-hour day (assume Poisson) a. Determine the average number of customers awaiting repairs. (Round your answer to 2 decimal places.) mber of customers b. Determine system utilization (Round your answer to the nearest whole percent. Omit the"%" sign in your response.) System utilization c. Determine the amount of time during an eight-hour day that the repaiman is not out on a call. (Use your rounded answer from Part b. Round your answer to 2 decimal places.) Amount of time hours d. Determine the probability of two or more customers in the system (Do not round intermediate calculations. Round your answer to 4 decimal places.) Probability Hints Reterences eBook & Resources Hint #1 Pinterest Veronical Check outExplanation / Answer
Service rate (S) = 2.5 hours per call or 0.4 calls per hour
Arrival rate (A) = 2.1 per eight hour day or 0.2625 calls per hour
a) Average number of customers waiting (Lq) = A^2/(S*(S-A)) = (0.2625)^2/(0.4*(0.4-0.2625) = 1.91
b) System Utilization = A/S = 0.2625/0.4*100 = 66
c) Amount of time not on call = (1-System Utilization%)*8 = (1-66%)*8 = 2.72 hours
d) Probability of two or more customers in system = (A/S)^2 = (0.2625/0.4)^2 = 0.4307
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