Final answer:
To maximize revenue for Boxed N Gone truck rentals, one must determine the maximum point on the revenue curve derived from the given price function, p(x) = 160 − 2x, by calculating the quantity of trucks to rent out and the corresponding price.
Step-by-step explanation:
The student wants to determine the optimal number of trucks to rent out and the price to charge to maximize revenue for Boxed N Gone truck rentals. Given the price function p(x) = 160 − 2x, where p represents the rental price for x number of trucks, we can find the maximum revenue by completing the square or using calculus to find the vertex of the parabola, which represents the maximum point on the revenue curve. Revenue, R(x), is calculated by multiplying the price function by the quantity of trucks rented, R(x) = x(160 − 2x). This forms a quadratic equation, and the revenue is maximized where the derivative R'(x) is zero. Solving R'(x) = 0 will give us the quantity of trucks that maximizes revenue, and substituting this quantity into the price function will provide the optimal rental price.
Following this approach will also help us find the maximum revenue. Since the overall objective is to maximize profit, understanding and applying this revenue maximization principle is key in fields such as business economics.