At the Order Fulfillment Center of a Major Mail-Order Firm

question 15

Essay

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?

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Definitions:

N Th Term

The expression that represents the term in a sequence or series that is in position "n", typically referred to in algebra and arithmetic sequences.

Binomial Coefficient

A value that represents the number of ways to choose a specified number of elements out of a set, often expressed as "n choose k".

Sum

The result of adding two or more numbers or quantities.

Binomial Theorem

A fundamental theorem in algebra that describes the algebraic expansion of powers of a binomial. According to the theorem, it's possible to expand the polynomial u200b\( (a + b)^n \)u200b into a sum involving terms of the form u200b\( a^k b^{n-k} \)u200b.