Write down the primal LP and dual LP for the MDP in the given figure $.$ Assume $=0\mathrm{.}9.$

Figure $1$: An MDP M$=($:S$,$A$,$P$,$R:$).$ The immediate rewards of all state$-$action

pairs are shown within square brackets. The state$-$transition probability of each

state$-$action pair is shown close to the arrows representing actions. Action a$\_(2)$ is

deterministic, so the probability $1$ is not shown in the figure.s$1$ to s$1$ action a$1$probability $0\mathrm{.}9.$ s$1$ to s$2$ action a$1$ probability $0\mathrm{.}1.$ s$2$ to s$2$ action a$1$ probability $0\mathrm{.}9.$s$2$ to s$3$ action a$1$ prob $0\mathrm{.}1.$ s$3$ to s$3$ action a$1$ prob $0\mathrm{.}9.$ s$3$ to s$1$ action a$1$ prob o$\mathrm{.}1.$ s$2$ to s$1$ action a$2$ reward$[2].$ s$3$ to s$1$ action a$2$ reward $[-1].$ s$1$ to s$1$ action a$2$ reward $[1]$