Question 242803
Joanne sells silk-screened T-shirts at community festivals and craft fairs. 
Her marginal cost to produce one t-shirt is $450.
Her total cost to produce 80 t-shirts is $420, and she sells them for $8 each.
a) find the linear cost function for joanne's t-shirt production
You have 2 points: (1,450), (80,420)
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slope = (420-450)/(80-1) = -30/79 
intercept: 450 = (-30/79)*1 + b
b = 450.38
C(x) = (-30/79)x+450.38
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b) How many t-shirts must she produce and sell in order to break even?
income = cost
8x = (-30/79)x+450.38
(8+(30/79))x = 450.38
x = 53.75
Round up to 54 t-shirts
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c) How many t-shirts must she produce and sell to make a profit of $900?
Solve 8x-[(-30/79)+459.38] = 900 for "x".
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Cheers,
Stan H.