Let x, y, z  be non integers  such x+y+z=12.  Then the maximum value of (xyz+xy+yz+zx)/16  is___.

xyz+xy+yz+zx  =(x+1)(y+1)(z+1)−(x+y+z)−1                              = abc−13 where a=x+1,  b=y+1,  c=z+1  are positive integers whose sum is 15. abc  is largest when a=b=c=5 Thus the answer is  5×5×−13=112 ∴xyz+xy+yz+zx16=11216=7