Joanne sells silk screened t shirts at a craft fair. Her marginal cost is 2.50. Her total cost to produce 50 t shirts is 215 and she sells them at 9 bucks each

Question

A. What is the linear cost function

B. How many must she produce and sell to break even

C. She must produce and sell how many to profit 500

Answer 1

50 * 2.15 = 107.50

250 - 107.5 = 142.5

(A) The cost function is C(n) = 142.50 + 2.5*N

(B) 9*N = 142.50 + 2.5*N

3.5* N = 142.50

N = 40 and 5/7

41 shirts to break even

(C) 9*N - ( 142.50 + 2.5 N) = 500

6.5N - 142.50 = 500

6.5N = 642.50

N = 98+

99 shirts to make $500 profit