A company owns vending machines located all over Toronto, which it resupplies from a central depot. Each vending machine is equipped with a sensor that alerts the company when it needs to be resupplied. On any given day, a machine raises an alert with probability . The company's resupply policy is purely corrective, i.e., it only resupplies the vending machines when it receives an alert. At the end of each day, the company compiles a list of the machines that raised an alert during that day and schedules a resupply for the next day. The company wants to study the number of resupplies it needs to perform. Assume that a machine does not push an alert on the same day that it was resupplied, and that the company has enough capacity to resupply as many machines as necessary in a day. a) Model this system as a Markov chain. State your assumptions explicitly, if any. b) Give an expression for the expected number of resupplies that the company will perform on a day in the long term.