Question #$10$: Consider a Leader$-$Follower duopoly, the firms face an $($inverse$)$ demand function: $Pb=109-5$ Qb$.$

The marginal cost for firm $1($The Leader$)$ is given by $mcl=3Q.$ The marginal cost for firm $2($The Follower$)$ is given by $mc2=7Q.$

$($Assume firm $1$ has a fixed cost of $$61$ and firm $2$ has a fixed cost of $$118.)$ How much of the total industry output is produced by firm $1?$

Hints $7\mathrm{.}65$