Let a = "How many metric tons per day furnace A produces",
    b = same for B,
    c = same for C.

Then you have these equations:

a   + b   + c   = 800,     (1)
a/2 + b/2 + c   = 545,     (2)
      b   + c/2 = 410.     (3)

Now multiply eq(2) by 2 (both sides), and then subtract eq(1) from it. You will get

a + b +  c  = 800          (1)
a + b + 2c = 1090          (4)
--------------------subtract      eq(1) from eq(4)

         c = 1090 - 800 = 290.

Having this, find b from (3).

Having b and c, find a from (1).