A monopolist's inverse demand function is estimated as $P=150-3Q.$ The company produces output at two facilities; the marginal cost of producing at facility $1$ is $M{C}_1(Q_1)=6Q_1,$ and the marginal cost of producing at facility $2$ is $M{C}_2(Q_2)=2Q_2.$

a$.$ Provide the equation for the monopolist's marginal revenue function. $($Hint: Recall that $Q_1+Q_2=Q.)$

$MR(Q)=$

$Q_1-Q_2$

$25$

b$.$ Determine the profit$-$maximizing level of outpyt for each facility.

Output for facility $1$ :

Output for facility $2$ :

c$.$ Determine the profit$-$maximizing price.

$