The music group Manga tours the country performing in different cities. A careful analysis of demand for

tickets to Manga concerts reveals a segmentation in the market. Demand for tickets by students is described

by $=500$

$$

$3$

$2$ while demand by those over $40$ years old is $=50$

$4$

$.$ If the marginal cost of a ticket

is $$3,$ how should tickets to Manga$$s concerts be priced to maximize profits?