Step 1 :Given the marginal-profit function \(P^{\prime}(x)=9x-1084\), where \(P^{\prime}(x)\) is in dollars per ticket and \(x\) is the number of tickets sold.
Step 2 :The total profit from the sale of the first 90 tickets is the integral of the marginal profit function from 0 to 90.
Step 3 :Calculate the integral of \(P^{\prime}(x)=9x-1084\) from 0 to 90 to find the total profit.
Step 4 :The total profit from the sale of the first 90 tickets is -61110 dollars.
Step 5 :However, it's unusual for a profit to be negative. This could mean that the costs associated with selling the tickets (such as production costs, marketing, etc.) are greater than the revenue from ticket sales.
Step 6 :Final Answer: The total profit from the sale of the first 90 tickets is \(\boxed{-\$61110}\).