Takao someya has developed flexible conductors from polymers and carbon nanotubes. these materials can be stretched up to 35% without losing structural integrity. this opens up the possibility for futuristic therapeutic devices, such as instrumented surgical gloves. when mixing two conducting species the overall conductivity is limited by the voigt-reuss bounds. the maximum conductivity is given by c_up = c_tubes v_tubes + c_poly v_poly the minimum is given by 1/c_down = v_tubes/c_tubes + v_poly/c_poly the exact relationship depends on how the two materials are mixed, but must be in between these two bounds. v_tubes is the volume fraction of nanotubes, v_poly is the volume fraction of polymer. the conductivity of the nanotubes is 1000 times greater than the polymer. at what volume fraction of nanotubes is the difference between the two bounds the greatest? at what volume fraction of nanotubes is the average between the two bounds 10 times greater than the conductivity of the polymer?