Answer
Daily fixed cost = $\$ 8,000$
Marginal cost = $\$ 25$ per bicycle
Work Step by Step
$C(x)=mx+b$
is called a linear cost function.
{\it T}he variable cost is $mx$ and the fixed cost is $b$.
The slope $m$, the marginal cost, measures the incremental cost per item.
With the given information, we observe two points on the graph of the cost function:
$(100,10500)$ and $(120,11000)$.
Calculate the slope:
$m=\displaystyle \frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{11,000-10,500}{120-100}=\frac{500}{20}=25$
(Marginal cost = $\$ 25$ per bicycle)
The cost function has form $C(x)=25x+b.$
To find b, substitute the coordinates of $(100,10500)$ and solve for $b.$
$10500=25(100)+b$
$10,500=2500+b\qquad/-2500$
$8,000=b$
(the daily fixed cost is $\$ 8,000$)
