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Joanne sells silk-screened T-shirts at community festivals and craft fairs. Her marginal cost to produce one T-shirt is $5.50. Her total cost to produce 70 T-shirts is $445, and she sells them for $9 each a. Find the linear cost function for Joannes 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 C(x)=

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Answer #1
a) The linear cost function = $60 + $5.5*x
Calculation:
Total marginal cost for 70 T-shirts = 70*5.5 = $       385
Fixed cost = $445-$385 = $          60
Hence, the above cost function.
b) Break even number of T-shirts = Fixed costs/Contribution margin per T-shirt = 385/(9-5.5) = 110 T-shirts
c) Number of T-shirts to be produced and sold to make profit of 600 = (Fixed cost+Desired profit)/Contribution margin per unit = (385+600)/(9-5.5) = 281.43
Rounded off to next whole number 282 T-shirts
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