Final answer:
The profit function p can be represented as p = -6x^2 + 280x - 1200. By substituting 1500 for p, we can solve for x in the equation 1500 = -6x^2 + 280x - 1200 to find the values of rolls at which the profit is $1500.
Step-by-step explanation:
The profit function, denoted as p, can be represented as p = -6x^2 + 280x - 1200.
This equation represents a quadratic function, where x represents the number of rolls and p represents the profit. The coefficients of the equation determine the shape of the graph and the maximum or minimum point, which represents the maximum profit.
In this case, the profit is $1500, so the equation p = 1500 can be used to find the corresponding value of x.
By substituting 1500 for p, we can solve for x in the equation.
1500 = -6x^2 + 280x - 1200
This equation can be simplified to a quadratic equation:
6x^2 - 280x + 2700 = 0
This equation can be further solved using factoring, completing the square, or the quadratic formula. The solutions for x will give the values of rolls at which the profit is $1500.