A monopolist$$s inverse demand function is estimated as P $=4503$Q$.$ The company produces output at two facilities; the marginal cost of producing at facility $1$ is MC$1($Q$1)=2$Q$1,$ and the marginal cost of producing at facility $2$ is MC$2($Q$2)=6$Q$2.$

a$.$ Provide the equation for the monopolist$$s marginal revenue function. $($Hint: Recall that Q$1+$ Q$2=$ Q$.)$

MR$($Q$)=$

$450$

$$

$6$

Q$1$

$6$

Q$2$

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

Instructions: Round your response to two decimal places.

Output for facility $1$:

$45$

Output for facility $2$:

$15$

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

Instructions: Round your response to the nearest penny $($two decimal places$).$

$

$270$