Question

The vertex is a minimum at (13,−50). The company actually loses money on their first few products as it costs them more to make them, but once they hit (blank/answer) items they break even again.

a) 0
b) 13
c) 26
d) 50

Answer 1

The company's minimum profit point is at (13, -50), indicating losses at that quantity of sales. To find the break-even point, the quantity must be doubled from the vertex, resulting in 26 items sold at which the company would break even. Hence, the correct choice is c) 26.

Step-by-step explanation:

The question asks about the point at which a company breaks even after initially losing money. The vertex of the parabola representing the company's profit model is given as a minimum at (13,−50). We know that the minimum point represents the lowest level of profit, which in this case is a loss, and that at some point after this minimum, the company must start breaking even. Since the vertex is at 13, this represents the lowest point. Therefore, the point at which the company breaks even again would be exactly the quantity at which total costs and total revenues are equal. Given that the vertex is the minimum point, the break-even quantity would be twice the quantity of the x-coordinate of the vertex to ensure it's on the opposite side of the parabola where profit is non-negative.

The correct answer is c) 26 as it is the double of the 13, indicating that when the company sells 26 items, total revenue will match the total costs, thus breaking even.