One local retail store in Chicago manages the inventory of washing machines using a (q, r) inventory policy. If the number of washing machines in stock decreases to 3 units, an order is placed with the manufacturer for 2 new washing machines. It takes a random amount of time for the order to be delivered to the retailer. If the inventory has at most 3 units when an order is delivered (including the newly delivered order), another order of 2 new washing machines is placed immediately. The delivery time of orders follows an exponential distribution with a rate of 3 units per time and the demand for the washing machines occurs according to an exponential distribution with a rate of 8 units per time. Demands that cannot be immediately met are lost. a) Model this problem as a continuous time Markov chain. b) What is the expected number of lost demands? c) What is the probability that the inventory is at full capacity? One local retail store in Chicago manages the inventory of washing machines using a (q, r) inventory policy. If the number of washing machines in stock decreases to 3 units, an order is placed with the manufacturer for 2 new washing machines. It takes a random amount of time for the order to be delivered to the retailer. If the inventory has at most 3 units when an order is delivered (including the newly delivered order), another order of 2 new washing machines is placed immediately. The delivery time of orders follows an exponential distribution with a rate of 3 units per time and the demand for the washing machines occurs according to an exponential distribution with a rate of 8 units per time. Demands that cannot be immediately met are lost. a) Model this problem as a continuous time Markov chain. b) What is the expected number of lost demands? c) What is the probability that the inventory is at full capacity? One local retail store in Chicago manages the inventory of washing machines using a (q, r) inventory policy. If the number of washing machines in stock decreases to 3 units, an order is placed with the manufacturer for 2 new washing machines. It takes a random amount of time for the order to be delivered to the retailer. If the inventory has at most 3 units when an order is delivered (including the newly delivered order), another order of 2 new washing machines is placed immediately. The delivery time of orders follows an exponential distribution with a rate of 3 units per time and the demand for the washing machines occurs according to an exponential distribution with a rate of 8 units per time. Demands that cannot be immediately met are lost. a) Model this problem as a continuous time Markov chain. b) What is the expected number of lost demands? c) What is the probability that the inventory is at full capacity? One local retail store in Chicago manages the inventory of washing machines using a (q, r) inventory policy. If the number of washing machines in stock decreases to 3 units, an order is placed with the manufacturer for 2 new washing machines. It takes a random amount of time for the order to be delivered to the retailer. If the inventory has at most 3 units when an order is delivered (including the newly delivered order), another order of 2 new washing machines is placed immediately. The delivery time of orders follows an exponential distribution with a rate of 3 units per time and the demand for the washing machines occurs according to an exponential distribution with a rate of 8 units per time. Demands that cannot be immediately met are lost. a) Model this problem as a continuous time Markov chain. b) What is the expected number of lost demands? c) What is the probability that the inventory is at full capacity