Owners of a bike rental company that charges customers between $5 and $25 per day have determined that the number ofbikes rented per day n can be modeled by the linear function n(p) = 150 – 6p, where p is the daily rental charge. Howmuch should the company charge each customer per day to maximize revenue? Do not include units or a dollar sign in youranswer.Provide your answer below:

Name: Owners of a bike rental company that charges customers between $5 and
Uploaded: 2024-03-20T07:07:26.000Z
Channel: Bartleby
Description: Owners of a bike rental company that charges customers between $5 and $25 per day have determined that the number ofbikes rented per day n can be modeled by the linear function n(p) = 150 – 6p, where p is the daily rental charge. Howmuch should the

Given: 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)==150-6p where p is the daily rental charge. Find the amount that company should charge each customer per day to maximize revenue as follows.First, find the revenue function as shown below. The revenue function is, Revenue function=Daily rental charge×Number of bikes rented per day=p×150-6p=150p-6p2 Therefore, the revenue function is Rp=150p-6p2 Compare the revenue function Rp=150p-6p2 with the parabola equation y=ax2+bx+c and obtain a=-6, b=150 and c=0. Here, a=-6<0. So, the vertex is the maximum of the function Rp=150p-6p2. The x coordinate of the vertex is, x=-b2a=15012=12.5The y coordinate of the vertex is, y=150p-6p2=15012.5-612.52=1875-937.5=937.5 Hence, the vertex of the revenue function is 12.5, 937.5. That implies, the maximum of the revenue function occurs at 12.5, 937.5. So, in order to maximize the revenue, the company should charge 12.5 dollars each customer per day . The answer is 12.5