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At the order fulfillment center of a major mail-order firm, customer orders, already packaged for shipment, arrive at the sorting machine to be sorted for loading onto the appropriate truck for the parcel's address. The arrival rate at the sorting machine is at the rate of 140 per hour following a Poisson distribution. The machine sorts at the constant rate of 150 per hour.
(a) What is the utilization rate of the system?
(b) What is the average number of packages waiting to be sorted?
(c) What is the average number of packages in the sorting system?
(d) How long must the average package wait until it gets sorted?
Population Studies
The scientific analysis of human populations, including their size, growth, density, and distribution, and the factors influencing these aspects.
Exponentially
Refers to a rapidly increasing rate of growth that becomes quicker and more intense as it progresses.
Arithmetically
Relating to or involving the use of arithmetic.
Linear Fashion
A sequential, straightforward manner of progression or development, moving from one stage directly to the next without deviation.
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