The area of △ABC is S=△ABP area +△ACP area +△BCP area =AB*x+BC*y+AC*z=5x+6y+7z.

That is, S=6m-y-2z x y z is greater than 0.

When y=z=0, the minimum value of m is S/6.

S=5m+y+2z

At this time, when y=z=0, m has the maximum value of S/5.