Products coming out of a production line are randomly sampled. Each hour one product is taken from the line and placed i

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Products coming out of a production line are randomly sampled.
Each hour one product is taken from the line and placed in a
reserved area for quality control. Quality control personnel checks
this area each hour. If there is only one product there, with
probability 0.6 they will take it for checking its quality,
otherwise they will leave it there. If there are two or more
products in the quality control area then, with probability 0.7
they will take two products (leaving the rest of them there) and
with probability 0.3 they will leave them all there. When there are
5 products in the quality control area, the personnel take them all
forsure to inspecting them. IN YOUR PDF DOCUMENT ANSWER THE
FOLLOWING: (a) Clearly define the states of this Markov process and
the transitions times (IMPORTANT NOTE: be very specific about the
transition times, i.e., if the variable is seen after the product
is placed in the quality control area or before). (5 pts) (b) Find
the one-step transition matrix. (12 pts) (c) If there is a cost of
$12 per hour per product left in the quality control area, What is
the expected long run cost for products in that area? (8 pts)