I am having trouble with this homework question

[daniel1211]

1. An NMOS transistor fabocated in a technology for
which k_n= 400e-6A/V^2 and V_t = 0.4 V is required to operate
with a small v_DS as a variable resistor ranging In value from
200 ohms to 1 k ohms. Specify the range required for the control voltage
V_GS and the required transistor width W. It is required to
use the smallest possible device, as limited by the minimum
channel length of this technology (L_min = 0.18e-6 m) and the
maximum allowed voltage of 1.8 V.
I have attached the work that I have done on this problem

 

[Valkarie]

.V_GS = 0.4V to 1.8VW = (1/400e-6A/V^2)*(V_GS - 0.4V)*(L_min) = (1/400e-6A/V^2)*(1.8V - 0.4V)*(0.18e-6m) = 10800 μm