Chapter 2.4, Problem 58E

Average cost. A company manufacturing snowboards has fixed costs of $\text{\$300}$ per day and total costs of $\text{\$5,100}$ per day at a daily output of $20$ boards.

(A) Assuming that the total cost per day, $C\left(x\right)$, 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 $\bar{C}\left(x\right)=C\left(x\right)/x$. Find the average cost function.

(C) Sketch a graph of the average cost function, including any asymptotes, for $1\le x\le 30$.

(D) What does the average cost per board tend to as production increases?