Question

T costs 16 dollars to manufacture and distribute a backpack. If the backpacks sell at x dollars each, the number sold, n, is given by n = 8x - 16/3(100 - x). Find the selling price that will maximize profit.

Answer 1

To determine the selling price that maximizes profit, the profit function (total revenue minus total cost) should be maximized by taking its derivative with respect to the selling price and finding the critical points. Without an explicit profit function, a numerical answer cannot be provided.

Step-by-step explanation:

The student asked to find the selling price that will maximize profit for a backpack that costs $16 to manufacture and is sold at x dollars each, with the relationship between the number sold, n, and the selling price being n = 8x - (16/3)(100 - x). In order to solve this problem, we would typically find the profit function, which is the total revenue minus total cost, and then take the derivative of the profit function with respect to x to find the critical points. The critical point(s) that result in the highest profit would be the optimal selling price(s). However, since the profit function itself is not given, we can only discuss the approach without providing a numerical answer. In general, firms aim to set a price where marginal revenue equals marginal cost to maximize profit.