To understand the cost function for the bookstore, let's break down the costs involved:
1. Fixed Costs: These are costs that do not change regardless of how many books are sold. For the bookstore, this is the daily cost to keep the store open, which is \[tex]$125.
2. Variable Costs: These are the costs that change with the number of books sold. For the bookstore, this is the cost per book, which is \$[/tex]16 per book.
To form the cost function [tex]\( C \)[/tex], we need to combine both the fixed costs and the variable costs.
Let:
- [tex]\( n \)[/tex] be the number of books sold in a day.
The total cost [tex]\( C \)[/tex] incurred by the bookstore can be expressed as:
[tex]\[ C = (\text{Fixed Daily Cost}) + (\text{Variable Cost per Book}) \times (\text{Number of Books Sold}) \][/tex]
Plugging in the given values:
[tex]\[ C = 125 + 16n \][/tex]
Where:
- The fixed daily cost = \[tex]$125
- The variable cost per book = \$[/tex]16
- [tex]\( n \)[/tex] is the number of books sold
So, the equation that represents the cost function for the bookstore is:
[tex]\[ C = 16n + 125 \][/tex]
Therefore, the correct answer is:
[tex]\[ \boxed{B. \ C = 16n + 125} \][/tex]
