At TEDxDelft2012, Dutch Aerospace Engineering student Boyan Slat unveiled a concept for removing large amounts of marine debris from the five oceanic gyres. With his concept called ‘Marine Litter Extraction’, he proposes a radical clean-up that would use the surface currents to let the debris drift to specially designed arms and collection platforms. This way the operation can be so efficient that it may even be profitable. According to Boyan Slat’s calculations, a gyre could realistically be cleaned up in five years’ time, collecting at least 7.25 million tons of plastic combining all gyres. He however does note that his concept would only apply for the top 2 meters, and a ‘radius’ of approximately 500 km, and will therefore have to be paired with ‘radical plastic pollution prevention methods in order to succeed’.
Method, a producer of household products, took the garbage patch as an opportunity and began marketing a dish soap whose container is made partly of recycled ocean plastic. The company sent crews to Hawaiian beaches to recover some of the debris that had washed up. 
Ok, lets assume it is 3 tons, or 6600 pounds, per km^2. One km^2 = 1000m by 1000m, or 1,000,000 m^2. According to my calculator, 6600 lbs spread equally among 1,000,000 sq meters, is 0.0066 lbs per sq meter, or 3 grams. You will find it profitable to sit out there and filter 600 lbs of seawater to remove 3 grams, 1/1000L, of plastic? Congratulations!