A company can produce T-shirts for $0.99 each. They spent $1,000,000 on their building and machines. What is the horizontal asymptotes of the graph that models the average cost of each t shirt, including the start up cost?

Answer 1

total cost for x shirts is

c(x) = 1000000 + .99x
average cost is
a(x) = c(x)/x = .99 + 1000000/x

asymptote at a = .99

makes sense, since for say, a billion shirts, they will each cost .99 + .001

(the fixed cost is shared among a billion shirts). The average cost will never get below .99, but will get closer and closer to it, as the fixed amount is spread among more and more shirts.