Joanne sells silk screened T shirts at community festivals

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 40 T - shirts is $150, and she sells them for $7 each. Find the linear cost function for Joanne\'s T - shirt production. How many T - shirts must she produce and sell in order to break even?. How many T - shirts must she produce and sell to make a profit of $700?. The linear cost function is C(x) = (Type your answer in slope - intercept form.). Joanne must produce and sell T - shirts in order to break even. Joanne must produce and sell T - shirts to make a profit of $700.

Solution

dC/dx = 2.50 dC = 2.50dx integrating both the sides, C(x) = 2.50x + C1 for x = 40, C(x) = 150 C1 = 50 a.) C(x) = 2.50x + 50 b.) C(x) = S(x) 2.50x + 50 = 7x x = 11 units c) Profit = sold-cost 700 = 7x - 2.50x - 50 x = 167 units