Consider the proabilistic DP example described in the DP lecture slides: production planning for the HIT-AND-MISS manufactuting company. Suppose the setup cost is now $4 whereas production cost reduced to $0.5 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. b. Find out the optimal policy and the optimal cost using probabilistic DP. c. Calculate the percentage improvement over the fixed policy if the optimal policy would be implemented. d. If the production cost would increase to $1.5 per item, do you think the percentage improvement over the fixed policy would be higher or lower than what you found in part c) ? Justify your answer.
