A firm in Eski$$ehir has a large sheep farm in which domestic sheep are bred for their meat peltry. Each year, $35\%$ of the newborn sheep: $65\%$ of the one$-$year$-$old sheep and $100\%$ of the two$-$ year$-$old sheep are slaughtered. The firm s policy is to breed its own newborn sheep to med the market demand: that is$,$ the firm does not purchase one$-$year$-$old or two$-$year$-$old sheep. For this purpose, the supply chain department of the firm determined that to meet the steady demands of the market, $15000$ newborn sheep must be added to the farm at the beginning of a typical year is also known that the cost of breeding a newborn sheep is a normal random variable with mean $400$ TL and standard deviation $50$ TL a one year old sheep $1$s a normal random variable with mean $360$ TL and standard deviation $30$ TL and a two$-$year$-$old sheep is a normal random variable with mean $320$ TL and standard deviation $25$ TL$.$

a$)$ Construct the Markov chain that is suitable to express the above$-$mentioned process

b$)$ Is the Markov chain you constructed in part $($a$)$ absorbing$?$ Explain in detail.

c$)$ What is the expected breeding cost for this farm in a typical year? $($Assume that the annual breeding cost is determined based on the determined based on the number of sheep on hand at the beginning of that year.$)$