Kemerköy Thermal Power Plant is a 630 MW coal-fired power station in Turkey in Balıkesir, Bandirma that uses lignite min

[answerhappygod]

Kemerköy Thermal Power Plant is a 630 MW coal-fired power
station in Turkey in Balıkesir, Bandirma that uses lignite
mined locally to produce electricity. The plant supplies its
lignite demand from five neighboring mines located in the villages
of Burhaniye, Edremit, Akçay, Altınoluk and Ayvalık. In order to
achieve economies of scales, weekly lignite requirements of the
plant are transferred from these villages to the plants warehouse
in lots of 500 tons only. That is, during a week, each village can
only send 500 tons or send nothing at all to the plant’s warehouse.
Based on historic observations, experts in the planning department
of the thermal plant claim that there is a probability p that each
village will be able to send 500 tons, hence the probability that a
village sends no lignite is 1-p. The plant works 6 days in a week
starting from Monday till Saturday. From past experience it is
known that the amount of lignite needed in weekly electric
production could be either 1000 or 1500 tons with equal
probabilities. At the end of each Saturday, the lignite inventory
level in the warehouse is observed by the planning department and
on Sundays, the villages send new lignite (if they will do so) to
the warehouse so that the plant starts Mondays with refreshed
amount of inventory. The capacity of the warehouse is 2500 tons and
the excess amount sent by the villages are brought to Yeniköy
Thermal Power Plant which is situated 20 km away from the warehouse
of Kemerköy Plant. Assume that the probability p that a village
will send a 500 tons of lignite lot to Kemerköy Plant’s warehouse
is computed as follows:
𝑝 = 0,33
Considering the information mentioned above, answer the
following questions:
1) Show that the change in lignite inventory levels in the
warehouse from week to week can be modeled as a Markov Chain.
Define the states and construct the one step probability transition
matrix. Explain how you calculate each transition probability (each
Pij).
2) If there are 1000 tons of lignite in the warehouse at the end
of November 20th, 2021, Saturday, find the probability that • there
will be 1500 tons of lignite in in the warehouse at the end of
November 27th, 2021, Saturday • there will be 2000 tons of lignite
in in the warehouse at the end of December 4th, 2021, Saturday •
there will be 1000 tons of lignite in in the warehouse at the end
of December 11th, 2021, Saturday
3) Now compute the corresponding transition matrix after 4, 5,
and 10 transitions? What can you conclude about the values you find
as the number of transitions increase? Explain in detail.
4) Find the classes for the one-step probability transition
matrix that you constructed in part (1). Define which states are
recurrent or transient.