Est. Budget: $1,000.00
Get a PIC18LF45K50 (or PIC18F45K50). Connect it to a PAN1323 module. Achieve 4096 Bytes per second data transmission in Bluetooth 3.0 (not BLE), using the HID profile in sniff mode, OR another protocol supported by iOS without the need to enter the MFi program (http://support.apple.com/kb/ht3647). You transmit to an android and iphone with a small test app to verify throughput. The entire circuit must consume less than 5mA. I offer 500$ for the android ...