Question

Owners of a bike rental company that charges customers between $5 and $25 per day have determined that the number of bikes rented per day n can be modeled by the linear function n(p)=450−18p, where p is the daily rental charge. how much should the company charge each customer per day to maximize revenue? do not include units or a dollar sign in your answer.

Answer 1

The company should charge $12.5 per day to maximize revenue, derived by setting the derivative of the revenue function to zero and solving for the price.

Step-by-step explanation:

To maximize revenue for the bike rental company with rental charges between $5 and $25 per day, we should find the rental charge p that maximizes the revenue function, which is R(p) = p × n(p). The function n(p) = 450 - 18p represents the number of bikes rented per day, where p is the daily rental charge. Revenue is maximized when the derivative of the revenue function with respect to p is zero (i.e., when the slope of the tangent line is flat). To find this,

We first express the revenue function as R(p) = p × (450 - 18p), which simplifies to R(p) = 450p - 18p^2. Then, we differentiate R(p) with respect to p to get R'(p) = 450 - 36p. Setting this equal to zero and solving for p yields 450 - 36p = 0 or p = 12.5. Thus, the company should charge $12.5 per day to maximize revenue.