Consider a Kyle $(1985)$ model where the true value of the stock is $$30,$ the unconditional variance of the true value is $25,$ the variance of uninformed trading is $3600$ and the unconditional expected value of the stock is $$25,$ i$.$e$.,$ E$[]=25,0(2)/(3)=25$

$1=30,02=3600.$

Please use this information to answer the following five questions.

$1)$The informed trader$$s optimal demand $($based on the model$)$ is:

$2)$The price impact is:

$3)$The informed trader's ex$-$ante profit is:

$4)$If noise trading u$=-20.$ then price p is:

$5)$Market maker's realized profit is$\_\_\_\_\_\_$ and informed trader's realized profit is $\_\_\_\_\_\_.$