Joanne sells silk-screened T-shirts at community festivals and craft fairs. Her

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 70 T-shirts is $245, and she sells them for $7 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 $600? a. The linear cost function is Cy)- b. Joanne must produce and sell T-shirts in order to break even. c. Joanne must produce and sell T-shirts to make a profit of $600

Explanation / Answer

standard linear function is

y = mx + b

245 = 70 ( 2.50 ) + b

b = 70

hence,

a) linear cost function is C(x) = 2.5x + 70

b) joanne sells each t shirt for $ 7

revenue function is 7x

7x = 2.5x + 70

x = 16

joanne must produce and sell 16 t shirts in order to break even

c) profit = 7x - 2.5x - 70

7x-2.5x - 70 = 600

4.5x = 670

x = 149

joanne must produce and sell 149 shirts to make a profit of $ 600

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