27.03.2023 - 16:06

# Joanne sells silk-screened T-shirts at community festivals and craft fairs. Her marginal cost to produce one T-shirt is $4.50 . Her total cost to produce 80 T-shirts is$ 410 and she sells them for $Joanne sells silk-screened T-shirts at community festivals and craft fairs. Her marginal cost to produce one T-shirt is$ 4.50 . Her total cost to produce 80 T-shirts is $410 and she sells them for$8 each. a. Find the linear cost function for Joanne’s T-shirt production. b. How many T-shirts must she produce and sell in order to break even c. How many T-shirts must she produce and sell to make a profit of $800? Answers (1) • April 9, 2023 в 21:28 a. To find the linear cost function, we need to first determine Joanne's fixed cost, which is the cost that does not depend on the number of T-shirts produced. We can find the fixed cost by subtracting the total variable cost from the total cost. Total variable cost = Marginal cost * Number of T-shirts produced Total variable cost =$4.50 * 80 = $360 Fixed cost = Total cost - Total variable cost Fixed cost =$410 - $360 =$50

So Joanne's linear cost function is: Cost = Fixed cost + (Marginal cost * Number of T-shirts produced) Cost = $50 + ($4.50 * N), where N is the number of T-shirts produced.

b. To break even, Joanne's revenue from selling T-shirts must equal her total cost. Her revenue per T-shirt is $8, so the number of T-shirts she needs to produce to break even is: Revenue = Cost$8N = $50 + ($4.50 * N) $3.50N =$50 N = 14.3

Since Joanne can't produce a fraction of a T-shirt, she needs to produce and sell at least 15 T-shirts to break even.

c. To make a profit of $800, Joanne's revenue from selling T-shirts must exceed her total cost by$800. Her revenue per T-shirt is $8, so the number of T-shirts she needs to produce to make a profit of$800 is:

Revenue - Cost = $800$8N - ($50 +$4.50N) = $800$3.50N = $850 N = 242.9 Since Joanne can't produce a fraction of a T-shirt, she needs to produce and sell at least 243 T-shirts to make a profit of$800.

Find the right answer to the question Joanne sells silk-screened T-shirts at community festivals and craft fairs. Her marginal cost to produce one T-shirt is $4.50 . Her total cost to produce 80 T-shirts is$ 410 and she sells them for \$ by subject Economics, and if there is no answer or no one has given the right answer, then use the search and try to find the answer among similar questions.