A monopolist$$s inverse demand function is P $=100$ Q$.$ The company produces output at two

facilities; the marginal cost of producing at facility $1$ is M C$1($Q$1)=4$Q$1,$ and the marginal cost of

producing at facility $2$ is M C$2($Q$2)=2$Q$2.$

$($a$)$ Provide the equation for the monopolist$$s marginal revenue function. $($Hint: Recall that Q$1+$

Q$2=$ Q$.)$

$($b$)$ Determine the profit$-$maximizing level of output for each facility.

$($c$)$ Determine the profit$-$maximizing price