For ABC stock, the trader at the XYZ Fund believes that if she buys at time t of Qt shares,the average price of the trade will be given by: Pt $=$ Pt$-1$ta $+0\mathrm{.}0002$ x It The most recent price is po $=$ $ $30.$ XYZ wants to buy $20,000$ shares. If a$=0\mathrm{.}1($that is$,$ the price is moving up$).$

$1)$The portfolio manager says that she would like the trade completed in two periods. The trading desk plans to execute equal amounts in each period:$10,000,$and $10,000,$what is the total cost?

$2)$

The optimal trading quantity in the first period is $\_\_\_\_\_$ and the second period is $\_\_\_\_\_\_.$ If the trades are optimally sized, the total cost is$\_\_\_\_\_.$

A$.$

$10,250$; $9,750$; $662,987\mathrm{.}5$

B$.$

$10,350$; $9,650$; $662,500$

C$.$

$10,250$; $9,750$; $661,950$

D$.$

$10,350$; $9,650$; $662,958\mathrm{.}5$