Chapter 4.2, Problem 1E

In Exercises 1-8, calculate total cost (disregarding any fixed costs) or total profit.

Total profit from marginal profit. A concert promoter sells x tickets and has a marginal-profit function given by

$P^{\prime }\left(x\right)=2x-150$,

where $P^{\prime }\left(x\right)$ is in dollars per ticket. This means that the rate of changes of total profit with respect to the number of ticket sold, x, is $P^{\prime }\left(x\right)$. Find the total profit from the sale of the first 300 tickets.