Answer
Daily fixed cost = $\$ 3000$
Marginal cost = $\$ 5$ per case
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:
$(1000,6000)$ and $(1500,8500)$.
Calculate the slope:
$m=\displaystyle \frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{8500-6000}{1500-1000}=\frac{2500}{500}=5$
(Marginal cost = $\$ 5$ per case)
The cost function has form $C(x)=$5$x+b.$
To find b, substitute the coordinates of $(1000,6000)$ and solve for $b.$
$6000=5(600)+b$
$6000=3000+b\qquad/-3000$
$3000=b$
(the daily fixed cost is $\$ 3000$)
