Question

A company manufactirung snowboards has fixed costs of $200 per day and total cost of $3800 per day at a daily output of 20 boards.
(A( Assuming that the total cost per day, C(x), is linearly related to the taotal out per dau,x, write an equation for the xost function
(B) The cost per board for an output of x boards is given by C(x)=C(x)/x, find the average cost function.
(C) What does the average cost per board tend to as production increases?
(D) sketch a graph of the average cost function, including any asympototes, for 1,=x,=30

Answer 1

A. The cost per 20 boards is 3800. so each board costs 3800/20 or $190. So the cost equation is C(x) = 200 + 190x

B. Divide the cost function by x. C(x)/x = 200/x + 190

C. The graph will be a curve that starts at (1,390) and curves down and to the right. Your last point will be at (30, 200/30+190) Your asymptote will be the horizontal line at 190 because as x tends to infinity, the term 200/x goes to zero. (There is also a vertical asymptote at x = 0 because you can't divide by zero, but your graph won't include x=0)

D. The average cost tends to 190 which was your horizontal asymptote.