Question $5($question on page $141-$HW$3$ modified$)$

A night$-$club owner has both student and adult customers. The demand for drinks by a typical student is $Q^S=18-3P.$ The demand for drinks by a typical adult is $Q^A=10-2$P$.$ There are equal numbers of students and adults. The marginal cost of each drink is $$2.$ Suppose the club owner can ask for identification card from its customers, and determine who among them is a student and who is not and, in turn, serve each group with a cover charge and a number of drinks tokens to each group $($so the owner is a monopolist and practices $1^{st}$ degree price discrimination$).$

$($a$)$ What will be the price per drink for the students? $(4\mathrm{.}4$ points$)$

$($b$)$ What will be the price per drink for the adults? $(4\mathrm{.}4$ points$)$

$($c$)$ What will be the number of tokens by students? $(4\mathrm{.}4$ points$)$

$($d$)$ What will be the number of tokens by adults? $(4\mathrm{.}4$ points$)$

$($e$)$ What will be the cover charge for the students? $(4\mathrm{.}4$ points$)$

$($f$)$ What will be the cover charge for the adults? $(4\mathrm{.}4$ points$)$