Suppose that clients arrive at a single$-$server system in accordance with a Poisson process with a rate of $.$ Upon arriving a client must pass through a door that leads to the server. However, each time someone passes through, the door becomes locked for the next $t$ units of time. An arrival finding a locked door is lost, and a cost $c$ is incurred by the system. An arrival finding the door unlocked passes through to the server. If the server is free, the client enters service; if the server is busy, the client departs without service and a cost $K$ is incurred. If the service time of a client is exponential with rate $,$ determine the average cost per unit time incurred by the system.