Final answer:
The question involves finding the price that maximizes profit for the Bluebird Bakery using a quadratic profit function. The given profit function is already in vertex form, indicating that the maximum profit occurs at a price of $0.45 per cookie, with a maximum profit of $400.
Step-by-step explanation:
The subject of this question is Mathematics, specifically focusing on using a quadratic profit function to determine the price that maximizes profit for the Bluebird Bakery. To maximize profits, we need to find the vertex of the given profit function, which is in the form of f(x) = -500(x - 0.45)^2 + 400. The vertex form of a quadratic equation is given as f(x) = a(x - h)^2 + k, where (h, k) is the vertex of the parabola.
In our case, the profit function already provides h = 0.45 and k = 400, indicating that the maximum profit occurs at a price of x = $0.45 per cookie, and the maximum profit is $400. To maximize profits, the bakery should therefore set the price of cookies to $0.45 each.