A company manufacturing surfboards has fixed costs of $300 per day and total costs of $5,100 per day at a daily output of 20 boards.
(A) Assuming that the total cost per day, C(x), is linearly related to the total output per day, x, write an equation for the cost function.
(B) The average cost per board for an output of x boards is given by C'(x)=C(x)/x. Find the average cost function.
(C) Sketch a graph of the average cost function, including any asymptotes, for x between 1 and 30.
(D) What does the average cost per board tend to as production increases?
A cost function is investigated and analyzed. The solution is detailed and well presented.