A question about LTSpice, quick help please

In LTSPICE, I've built a pseudo-NMOS inverter and I've got 2 tasks to do using it.

1) I've a initial guess for Wn value of NMOS. I start the simulation with this value however, I need to optimize it and get a more precise value.

Basically, when Vol < x for some x, I need to find the minimum Wn value that satisfies this inequality.

2)Initially, nothing is connected to the output of inverter. Then, I connect a capacitor after finding my Wn value. At this point I need to find LOW-to-HIGH delay of the inverter.

I think I need a DC sweep for the first one. But don't know how to extract my value.

I have no idea for the second one though.

Any help is much appreciated.

For finding the time delay you would use the Transient response simulation. Click on the input and output nodes to plot their waveforms. Double-click on the node names at the top of the plot to generate two cursors to measure the delta time between the input and output signals.

I just got this one. Still working on first one though.