1. Comet Dry Cleaners specializes in same-day dry cleaning. Customers drop off their garments early in the morning and expect them to be ready for pickup on their way home from work. The risk is, however, that the work needed on a garment cannot be done that day, depending on the type of cleaning required. Historically, an average of 20 garments have had to be held over to the next day. The outlet’s manager is contemplating expanding to reduce or eliminate that backlog. A simulation model was developed with the following distribution for garments per day: Number Probability Random Numbers 50 0.10 00–09 60 0.25 10–34 70 0.30 35–64 80 0.25 65–89 90 0.10 90–99 With expansion, the maximum number of garments that could be dry-cleaned per day is: Number Probability Random Numbers 60 0.30 00–29 70 0.40 30–69 80 0.30 70–99 In the simulation for a specific day, the number of garments needing cleaning (NGNC) is determined first. Next, the maximum number of garments that could be dry-cleaned (MNGD) is determined. If MNGD Ú NGNC, all garments are dry-cleaned for that day. If MNGD 6 NGNC, then (NGNC - MNGD) garments must be added to the number of garments arriving the next day to obtain the NGNC for the next day. The simulation continues in this manner. a. Assuming that the store is empty at the start, simulate 15 days of operation. Use the following random numbers, the first determining the number of arrivals and the second setting the capacity: (49, 77), (27, 53), (65, 08), (83, 12), (04, 82), (58, 44), (53, 83), (57, 72), (32, 53), (60, 79), (79, 30), (41, 48), (97, 86), (30, 25), (80, 73) Determine the average daily number of garments held overnight, based on your simulation. b. If the cost associated with garments being held over is $25 per garment per day and the added cost of expansion is $200 per day, is expansion a good idea
Compound Probability
Compound probability can be defined as the probability of the two events which are independent. It can be defined as the multiplication of the probability of two events that are not dependent.
Tree diagram
Probability theory is a branch of mathematics that deals with the subject of probability. Although there are many different concepts of probability, probability theory expresses the definition mathematically through a series of axioms. Usually, these axioms express probability in terms of a probability space, which assigns a measure with values ranging from 0 to 1 to a set of outcomes known as the sample space. An event is a subset of these outcomes that is described.
Conditional Probability
By definition, the term probability is expressed as a part of mathematics where the chance of an event that may either occur or not is evaluated and expressed in numerical terms. The range of the value within which probability can be expressed is between 0 and 1. The higher the chance of an event occurring, the closer is its value to be 1. If the probability of an event is 1, it means that the event will happen under all considered circumstances. Similarly, if the probability is exactly 0, then no matter the situation, the event will never occur.
1. Comet Dry Cleaners specializes in same-day dry cleaning.
Customers drop off their garments early in the morning
and expect them to be ready for pickup on their way home
from work. The risk is, however, that the work needed
on a garment cannot be done that day, depending on
the type of cleaning required. Historically, an average of
20 garments have had to be held over to the next day. The
outlet’s manager is contemplating expanding to reduce
or eliminate that backlog. A simulation model was developed with the following distribution for garments per day:
Number Probability Random Numbers
50 0.10 00–09
60 0.25 10–34
70 0.30 35–64
80 0.25 65–89
90 0.10 90–99
With expansion, the maximum number of garments that
could be dry-cleaned per day is:
Number Probability Random Numbers
60 0.30 00–29
70 0.40 30–69
80 0.30 70–99
In the simulation for a specific day, the number of garments
needing cleaning (NGNC) is determined first. Next, the
maximum number of garments that could be dry-cleaned
(MNGD) is determined. If MNGD Ú NGNC, all garments
are dry-cleaned for that day. If MNGD 6 NGNC, then
(NGNC - MNGD) garments must be added to the number
of garments arriving the next day to obtain the NGNC for
the next day. The simulation continues in this manner.
a. Assuming that the store is empty at the start, simulate
15 days of operation. Use the following random numbers, the first determining the number of arrivals and
the second setting the capacity:
(49, 77), (27, 53), (65, 08), (83, 12), (04, 82),
(58, 44), (53, 83), (57, 72), (32, 53), (60, 79),
(79, 30), (41, 48), (97, 86), (30, 25), (80, 73)
Determine the average daily number of garments held
overnight, based on your simulation.
b. If the cost associated with garments being held over is
$25 per garment per day and the added cost of expansion is $200 per day, is expansion a good idea?
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