PSAT Math Grid-Ins Question 17: Answer and Explanation

Question: 17

The profit that a donut shop makes can be expressed by the equation P = -4(x - 3)² + 2,000, where x is the price per donut sold (in dollars). What price, in dollars, should the donut shop charge its customers in order to maximize its profit?

Correct Answer: 3

Explanation:

3

The question asks for the price per donut, x, that a donut shop should charge to maximize its profit, P. To see the maximum, the quadratic must be in vertex form since the vertex is that value. The vertex form is y = a(x - h)² + k, in which (h, k) is the vertex. The equation given in the question is P = -4(x - 3)² + 2,000, which is already in vertex form, so the vertex is (3, 2,000). The x-coordinate is the price, so the shop should charge $3. The correct answer is 3.