Suppose that the average stock price is expected to move as:

Pt $=$ Pt$-1+0\mathrm{.}001$ X St$,$ where St is the number of shares bought $($or$,$ if negative, sold$),$and the current price is p$.=$ $$20.$

$1)$What is the total sale proceeds if $1200$ shares are sold in trades of $600,300,$ and $300$ shares?

$2)$What is the total sale proceeds if the three trades are optimally sized?