Question

Joanne sells silk-screened T-shirts at community festivals and craft fairs. Her marginal cost to produce one t-shirt is $2.50. Her total cost to produce 50 t-shirts is $215, and she sells them for $9 each.

Find the linear cost function for Joanne's t-shirt production.

Answer 1

The linear cost function for Joanne's t-shirt production is C(x) = $2.50x + $90.

Step-by-step explanation:

To find the linear cost function for Joanne's t-shirt production, we need to determine the fixed cost and the variable cost per t-shirt. We are given that her total cost to produce 50 t-shirts is $215, so we can subtract the variable cost (50 x $2.50 = $125) to find the fixed cost, which is $215 - $125 = $90.

Now we have the fixed cost and can use the formula for a linear cost function: C(x) = mx + b, where C(x) represents the total cost, x represents the number of t-shirts, m represents the variable cost per t-shirt, and b represents the fixed cost.

Substituting the values we have, the linear cost function for Joanne's t-shirt production is C(x) = $2.50x + $90.