Question

A manufacturer of surfboards has fixed costs of $300 per day and a total cost 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

Answer 1

Answer:

a) $C(X) =240 x +300$

b) $C'(X) =\frac{240x +300}{x}= 240 +\frac{300}{x}$

Step-by-step explanation:

Part a

For this case we need to find a linear model like this one:

$C(X) = m x +b$

We assume that the fixed costas are 300 per day so then the value of b = 300

$C(X) = m x+300$

And then we can use the other condition $C(20) = 5100$

And we can find the value for the slope like this:

$5100= m (20) +300$

$4800 = 20 m$

$m =\frac{4800}{20}=240$

So then the lineal model would be given by:

$C(X) =240 x +300$

Part b

For this case we defined the cost per board like this:

$C'(X) = C(X)/x$

So we just need to divide the function that we found on part a by x and if we do this we got:

$C'(X) =\frac{240x +300}{x}= 240 +\frac{300}{x}$