Feasibility of project with 50 leds working independently
depending on how you want to control your LED's there are several options.
firstly to be clear you could not feasibly connect that many LEDs to an arduino that could all be turned on at once (if that was needed) without damaging the arduino.
if all you need is on/off level of control then you could look at shift registers or if you have pre built arrays of LEDS in a grid type layout you could look at the MAX7219/MAX7221
if you also wanted to be able to control the brightness individually then you could look at the TLC5940
if we look at the pros and cons of each approach:
74HC595
pros:

cheap to buy
simple to use

cons:

each LED needs its own resistor
cannot vary brightness
if not using the hardware SPI pins can be slow for large numbers of outputs

MAX7219/MAX7221
pros:

lower current draw than 74HC595
only needs one resistor per IC which can drive 64 LEDs

cons:

actually flashes LED's really fast to look like they are always on
costs more than 74HC595

TLC5940
pros:

can vary brightness with a high number of steps (4096 steps from fully off to fully on)

cons:

uses more output pins than either of the above methods
requires resistor per LED
costs more for the IC than 74HC595

so to sum up, each method has its merits. if you are driving individual LEDs the the 74HC595 is probably the best/simplest route, if you are driving an array then the MAX7219/MAX7221 is best, and if you need variable brightness then the TLC5940 is probably best.