Question

Jaden is selling tickets to a show his band is headlining. He knows from ticket sales for the last few shows they have done that their profits can be modeled by the function, where P(x)=-1/16x²+24x+20 is the profit and is the number of tickets sold. How many tickets should Jaden sell so that he gets the maximum profit? What is that profit? What is the profit per ticket at this rate?

Answer 1

Jaden should sell 192 tickets to get a maximum profit of $1352. The profit per ticket at this rate is $7.04.

Step-by-step explanation:

To find the number of tickets Jaden should sell in order to maximize profit, we need to find the vertex of the function that models their profit. The profit function is given by P(x) = -1/16x^2 + 24x + 20, where x represents the number of tickets sold.

The vertex of this function can be found using the formula x = -b/2a, where a, b, and c are the coefficients of the quadratic function. In this case, a = -1/16, b = 24, and c = 20. Plugging these values into the formula, we get x = -24 / (2 * (-1/16)) = 192 tickets.

So, Jaden should sell 192 tickets to maximize profit. To find the maximum profit, we plug this value of x back into the profit function: P(192) = -1/16(192)^2 + 24(192) + 20 = 1352.

Therefore, Jaden should sell 192 tickets to get a maximum profit of $1352.

The profit per ticket at this rate can be found by dividing the maximum profit by the number of tickets sold: 1352 / 192 = $7.04 per ticket.