Problem 5 Consider the following blood inventory problem facing a hospital. There is need for a rare blood type, namely, type AB, Rh negative blood. The demand D (in pints) over any 3-day period is given by: P{D = 0) = 0.4, PID = 1) = 0.3, P{D = 2) = 0.2, and PID= 3) = 0.1. Note that the expected demand is 1 pint, since E(D) =0.3(1) +0.2(2) +0.1(3) = 1. Suppose that there are 3 days between deliveries. The hospital proposes a policy of receiving 1 pint at each delivery and using the oldest blood first. If more blood is required than is on hand, an expensive emergency delivery is made. Blood is discarded if it is still on the shelf after 21 days. Denote the state of the system as the number of pints on hand just after a delivery. Thus, because of the discarding policy, the largest possible state is 7. a) b) c) Follow the 3-step process to model the problem as a Markov Chain. To receive full credit, include the transition probability diagram. Find the steady-state probabilities of the state of the Markov chain Use the steady-state probabilities to determine the probability that a pint of blood will need to be discarded during a 3-day period. (Hint: because the oldest blood is used first, a pint reaches 21 days only if the state was 7 and then D=0. Use the steady-state probabilities to determine the probability that an emergency delivery will be needed during the 3-day period between regular deliveries. d)