An extremely low cost wireless keyboard and mouse set from Logitech, namely the Logitech MX220, goes for about USD20 but suffers from signal issues (possibly interference). Logitech wireless peripherals communicate over and could possibly be interfered with by wireless equipment. In any case, the MX220 set has been observed to fail at about range, the mouse losing its connection to the receiver plugged into the PC.
Opening the receiver with a dremel (no easy way) and inspecting the circuitry one can notice that the device has a printed antenna on the PCB. Using a tool to scrape off the PCB overlay, the antenna trace can be exposed sufficiently in order to be able to extend the antenna with a cable of appropriate length.
After the fix, tests have been performed and the mouse seems to behave normally without losing its connection to the receiver. A different, perhaps better, fix could have been to increase power to the transmitter but that would have required reworking the circuitry.