Question

Profit, Revenue, Costs
Maria paints custom tote bags and sells them at a community

$3.50
fair. She uses the equation

$31.50
P = 12n - (3.5n + 40)

$40.00
to calculate her total profit, in dollars, when she sells n tote bags.

$43.50
What are Maria's total costs for making just one tote bag?

Answer 1

To solve for Maria's total costs for making just one tote bag, we need to analyze the profit equation she uses:

\[ P = 12n - (3.5n + 40) \]

Here:

- \( P \) is the total profit.
- \( n \) is the number of tote bags sold.
- \( 12n \) represents the total revenue from selling \( n \) tote bags at $12 each.
- \( (3.5n + 40) \) represents the total costs, which consist of $3.50 per tote bag plus a fixed cost of $40.

To find the total cost of making one tote bag, we will look specifically at the costs associated with producing that one tote bag:

1. The cost of producing one tote bag is $3.50.
2. The equation also includes a fixed cost of $40 that does not depend on the number of tote bags produced.

The total cost structure can be expressed as:

\[ \text{Total Costs} = 3.5n + 40 \]

For \( n = 1 \) (for just one tote bag):

\[
\text{Total Costs for 1 tote bag} = 3.5(1) + 40 = 3.5 + 40 = 43.5
\]

So, Maria's total costs for making just one tote bag (including both the variable and fixed costs) is **$43.50**.