A $87$ kg patient was given $7$ mg$/$kg$/$day for some time and the average plasma concentration was measured as $8$ mg$/$L$.$ Since this was too low, the dose was raised to $10$ mg$/$kg$/$day$.$ Unfortunately this resulted in an average plasma concentration of $24$ mg$/$L$.$ Calculate Vm and Km and then calculate a dose rate which should achieve an average plasma concentration of $16$ mg$/$L$.$