1) Part X is a slow-moving part with the demand distribution given in the table below. Assume that replenishment orders placed for part X at the end of the day are fulfilled by the beginning of the next day. Consider a Q = 3, R = 0 order policy for part X. Assume backorders are possible, and are fulfilled the next day.
Demand Probability
0 80%
1 10%
2 10%
a. What is the transition matrix for the inventory level of part X (assume the state is measured at the end of the day, after demand is realized and before replenishment is received)?
b. What is the average inventory of part X?
c. What percentage of the time will there be a backorder for part X?
Please solve and show the steps to the solution.