The profit analysis of a single server two-unit (one priority and the other ordinary) cold standby system with two modes normal and total failure is examined. The priority unit gets preference both for operation and repair. Whenever an operative unit fails, a delay occurs in locating the repairman and getting him to the system location due to certain administrative actions with known probability p. The system is observed at suitable regenerative epochs in order to obtain several economics-related reliability characteristics. Explicit results are obtained in a few particular cases.