To determine the cost function for Natalie's clothing store per month, we need to consider both the variable costs (those that change with the number of shorts sold) and the fixed costs (those that remain constant regardless of the number of shorts sold).
1. Variable Costs:
- Cost per pair of shorts: \[tex]$7
- Cost per box for shorts: \$[/tex]3
- Cost per bag: \[tex]$0.25
However, we need to find the combined variable cost per pair of shorts, which we'll call \( n \):
\[
\text{Variable cost per short} = \text{Cost per short} + \text{Cost per bag} = 7 + 0.25 = 7.25
\]
Therefore, for \( n \) shorts, the total variable cost will be:
\[
7.25n
\]
2. Fixed Costs:
- Rent: \$[/tex]650
- Electricity: \[tex]$55
- Advertising: \$[/tex]20
Summing these fixed costs gives us the total fixed cost per month:
[tex]\[
\text{Total fixed cost} = 650 + 55 + 20 = 725
\][/tex]
Combining the variable costs and fixed costs, we can construct the cost function [tex]\( C \)[/tex] for Natalie's store per month as follows:
[tex]\[
C = 7.25n + 725
\][/tex]
Thus, the cost function that represents Natalie's monthly costs in terms of the number of pairs of gym shorts [tex]\( n \)[/tex] is:
[tex]\[
\boxed{C = 7.25n + 725}
\][/tex]
This matches option A. Therefore, the correct cost function is:
[tex]\[
\text{A. } C = 7.25n + 725
\][/tex]
