b $.$ ?A budget of $5000$ ?is shared by $3$ ?teams, i $.$ e $.,$ ?Teams $A,B$ ?and $C$ ?get $2500,1500$ ?and $1000,$ ?respectively. In every $2$ ?years, the budget of each team will be redistributed according to the following strategy.

Team A: $20\%$ ?and $35\%$ ?of the current Team $A\text{'}$ s share will be transferred to Team $B$ ?and Team $C,$ ?respectively. The remaining is left for itself.

Team B: $40\%$ ?and $10\%$ ?of the current Team $B\text{'}$ s share will be transferred to Team A and Team $C,$ ?respectively. The remaining is left for itself.

Team C: $15\%$ ?and $25\%$ ?of the current Team $C\text{'}$ s share will be transferred to Team A and Team $B,$ ?respectively. The remaining is left for itself.

i $.$ ?Draw a Markov chain to model the budget transitions between teams with the information of transition probability.

$[6$ ?marks $]$

ii $.$ ?How much of the budget originally given to Team A will Team $C$ ?receive after $4$ ?years?

$[4$ ?marks $]$

iii. How much budget will Team A receive in the long run as $t???$

$[5$ ?marks $]$