Question

The management of a company that manufactures roller skates has fixed costs (costs at 0 output) of $300 per day and total costs of $4,300 per day at an out put of 100 pairs of skates per day. Assume that cost C is linearly related to output x, find the equation of the line relating output to cost.

Answer 1

For the given question:

Assume that cost C is linearly related to output x

The general equation will be:

$c=ax+b$

where: (a) and (b) are constants

Given:

The fixed costs (costs at 0 output) of $300 per day

That means: c = 300 when x = 0

so,

$\begin{gathered} 300=a\cdot0+b \\ b=300 \end{gathered}$

So, the equation will be:

$c=ax+300$

And given:

The costs of $4,300 per day at an output of 100 pairs of skates per day.

So, c = 4300 when x = 100

so,

$4300=a\cdot100+300$

solve the equation to find (a)

$\begin{gathered} 100a=4300-300 \\ 100a=4000 \\ a=\frac{4000}{100}=40 \end{gathered}$

So, the answer will be:

The equation of the line relating output to cost is:

$c=40x+300$