Consider the following cheese inventory problem facing a Prof. Smith's cheese-making business. There is demand for a smoked Gouda that takes her a particularly long time to make. The demand D (in ounces) over any 3 day period is P(D = 0) = 0.4 P(D = 1) = 0.3 P(D = 2) = 0.2 P(D = 3) = 0.1 Suppose that it takes three days to make more Gouda. The business proposes a policy of making 1 ounce in each production cycle and selling the oldest cheese first. If more cheese 1 Due October 28, 2019 Homework 5 ISyE 320 is required than is on hand, then an expensive outsourcing request is made. Cheese is discarded if it is still on the shelf after 21 days. Denote the state of the system Xt as the number of ounces on hand just after a production cycle. (Thus, because of the discarding policy, Xt {0, 1, 2, 3, 4, 5, 6, 7}). Problem 3.1 What is the expected demand for Gouda? Problem 3.2 What is the variance of the demand? Problem 3.3 Construct the one-step transition matrix for this Markov Chain