A textile finishing process involves drying a fabric that has been treated with a volatile solvent. The wet fabric entering the
dryer contains 45% solvent, and the dried fabric contains 3% of the entering solvent. Solvent-free air enters the dryer at a rate of 8 pounds per pound of solvent-free fabric. The solvent has a molecular weight of 60 g mol-1. (a) Calculate the percentage of solvent in the dried fabric by weight. (Answer: 2.4%) (b) Calculate the concentration of solvent in the dryer exhaust in mg m-3 if the exhaust is at 160 F and 1.0 atm.
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Answer:
the average number of customers awaiting repairs = 0.30
the system utilization = 42
the amount of time that the repairman is not out on a call is = 4.64 hours
the probability of two or more customers in the system = 0.1764
Explanation:
Given that :
Repair time, including travel time = mean of 1.6 hours per call.
Requests for copier repairs = mean rate of 2.1 per eight-hour day
i.e mean rate R = 2.1/day
Time = 8 hours
thus; mean rate μ = 8 hours/ 1.6 hours = 5
(a)
Let the average number of customers awaiting repairs be :
the average number of customers awaiting repairs = 0.30
(b) Determine system utilization.
The system utilization is determined as follows:
(c) The amount of time during an eight-hour day that the repairman is not out on a call is calculated as :
Percentage of Idle time = 1 -
Percentage of Idle time = 1 - 0.42
Percentage of Idle time = 0.58
However during an 8 hour day; The amount of time that the repairman is not out on a call is = 0.58 × 8 = 4.64 hours
(d)
the probability of two or more customers in the system by assuming Poisson Distribution is:
P(N ≥ 2) = 1 - (P₀+ P₁)
where;
P₀ = 0.58
P₁ = 0.58 × 0.42 = 0.2436
P(N ≥ 2) = 1 - ( 0.58 + 0.2436)
P(N ≥ 2) = 1 - 0.8236
P(N ≥ 2) = 0.1764
Thus; the probability of two or more customers in the system is 0.1764