Lynton runs a rental shop for dirt bikes. He currently charges $60 per bike rental, and he averages 25 rentals per day. Lynton has been experimenting with his rental price, and he knows that for every 5 dollars he raises the rental price, he loses 3 customers per day. Lynton wants to change his rental price in order to maximize his income. Lynton’s profit can be estimated with the equation P(x)=(60+5x)(25−3x). Use the profit formula to answer Part A and Part B.

Part A: Which answer choice correctly explains approximately how much Lynton should charge per bike rental to maximize his profit?

Part B: How much will Lynton earn per day if he maximizes his profit?

Select one answer for Part A and one answer for Part B.
B: $1348.79
A: Lynton should charge approximately $51 per rental. To determine this, Lynton can use P(x) to locate the x-coordinate of the maximum (max), which is −1.83. This indicates that Lynton should decrease his price by 1.83 times 5 dollars, which is about 9 dollars. Thus, Lynton should charge about $51 per rental to maximize profit.
B: $1500.00
A: Lynton should keep his rental price at $60. To determine this, Lynton can use P(x) to locate the x-coordinate of the maximum (max), which is −1.83. It is not logical for Lynton to lower his price, which means Lynton is already maximizing his profit. Thus, Lynton should charge $60 dollars per rental to maximize profit.
A: Lynton should charge approximately $62 per rental. To determine this, Lynton can use P(x) to locate the y-coordinate of the maximum (max), which is 1,550.42. This indicates the profit Lynton can make daily. Divided by the average of 25 rentals per day, this yields $62.02. Thus, Lynton should charge about $62 dollars per rental to maximize profit.
B: $1277.30
A: Lynton should charge approximately $58 per rental. To determine this, Lynton can use P(x) to locate the x-coordinate of the maximum (max), which is −1.83. This indicates that Lynton should decrease his price by 1.83 dollars, which is about 2 dollars. Thus, Lynton should charge about $58 per rental to maximize profit.
B: $1,550.42