Part $1(2$ points$)$

Two Cournot duopolists compete in a market with inverse demand given by $p=209\mathrm{.}00-2Q,$ where $p$ is the per$-$unit price, $q_i$ is the output for firm $i($either firm $1$ or firm $2),$ and $Q=q_1+q_2.$ Firm $1$ has a cost function of $c_1(q_1)=2q_1^2$ and firm $2$ has a cost function of $c_2(q_2)=3q_2^2.$ Assume no fixed costs.

What is the optimal output for firm $1?$

$($Round to two decimals if necessary.$)$

What is the optimal output for firm $2?$

$($Round to two decimals if necessary.$)$

Part $2(1$ point$)$

What is the equilibrium price in this market? $

$($Round to two decimals if necessary.$)$

Part $3(2$ points$)$

What is the profit for each firm?

Firm $1$ profit: $$,($Round to two decimals if necessary.$)$

Firm $2$ profit: $$,($Round to two decimals if necessary.$)$N