Has just started producing blue smoke at the.

At engine start-up or all the time it's running? If it stops after a minute or two after starting the engine it is likely in need of valve guide seals. If it does it all the time it could also be a stuck / broken / worn piston ring. Also check the oil for signs of being diluted with raw gas. If the oil is diluted and it's real thin and runny, have it changed right away. Have the pcv valve inspected too to be sure it's not allowing pressure to build up in the bottom of the engine. That will push the oil on the cylinders past the oil control rings. Evidence of that would be found on the spark plugs as a black residue. If that is only found on one spark plug, suspect piston rings or valve guide seals. If it's found on all spark plugs, suspect the pcv valve.