Suppose the setup cost is now $$5\mathrm{.}5$ whereas production cost reduced to $$0\mathrm{.}5$ per item. You are informed that the company always follows a fixed policy: $(4,3,3)($i$.$e$,$ producing $4,3,$ and $3$ items for runs $1,2,$ and $3$ respectively$),$ without taking into account the inherent stochasticity. a$.$ Calculate the expected cost incurred for the fixed policy. $(20$ points$)$ b$.$ Find out the optimal policy and the optimal cost using probabilistic DP$.(70$ points$)$ c$.$ Calculate the percentage improvement over the fixed policy if the optimal policy would be implemented. $(10$ points$)$