Question

How can Kate use the data on the prices and associated profits of the A100 bike model over the last three months to determine the selling price that will allow Cycling Incorporated to maximize its profits?

A. Kate should calculate the average profit and set the selling price to maximize this average.
B. Kate can identify the vertex of the quadratic model to find the selling price for maximum profits.
C. Kate should focus on the highest profit month and set the selling price to match that month's price.
D. Kate can use the total profit over the three months to determine the optimal selling price.

Answer 1

Kate should identify the vertex of the quadratic model to determine the optimal selling price that maximizes profits on the A100 bike model, rather than relying on averages or total profit calculations.

Step-by-step explanation:

To determine the selling price that will allow Cycling Incorporated to maximize its profits on the A100 bike model using the data from the last three months, Kate should opt for option B: she can identify the vertex of the quadratic model that represents the relationship between selling price and profit. By finding the vertex of the quadratic equation, where the value of the function is at its maximum, Kate will be able to ascertain the optimal selling price that maximizes profits.

This approach is based on the fact that the relationship between price and profit in such scenarios often forms a parabolic shape (a quadratic function) on a graph, where the highest point, or vertex, represents the maximum profit. Other options, like calculating averages or adding total profits, might provide some insights, but they do not reliably indicate the price that will yield the maximum possible profit.