Question

A concert promoter sells tickets and has a​ marginal-profit function given​ below, where Upper P prime (x )is in dollars per ticket. This means that the rate of change of total profit with respect to the number of tickets​ sold, x, is Upper P prime (x ). Find the total profit from the sale of the first 480 ​tickets, disregarding any fixed costs.

Answer 1

To find the total profit from the sale of the first 480 tickets, we need to calculate the integral of the marginal-profit function and evaluate it.

Step-by-step explanation:

To find the total profit from the sale of the first 480 tickets, we need to calculate the integral of the marginal-profit function. Since the marginal-profit function gives the rate of change of total profit with respect to the number of tickets sold, integrating it will give us the total profit.

Let's assume the marginal-profit function is given by P'(x). To find the total profit, we integrate P'(x) with respect to x from 0 to 480. This can be written as:

Total Profit = ∫ P'(x) dx

Once we have the integral, we can evaluate it to find the total profit.