Part $1(2$points$)$

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Two Cournot duopolists compete in a market with inverse demand given by $=56\mathrm{.}002$p$=56\mathrm{.}002$Q$,$ where $$p is the per$-$unit price, $$qi is the output for firm$$i $($either firm $1$ or firm $2),$ and $=1+2$Q$=$q$1+$q$2.$ Both firms face constant marginal costs of $$2$ per unit. 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$)$

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What is the equilibrium price in this market?$$$$($Round to two decimals if necessary.$)$

Part $3(2$points$)$

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What is the profit for each firm?

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

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