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)
  • don1kostelano
    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.

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