#### Answer

a) $C(x)=4.75x+500.000$;
b) $b=500.000$;
c) $975.000$;
d) $4.75$

#### Work Step by Step

a) Since the cost function is linear, it can be expressed in the form $C(x)=mx+b$
To find each elements in the formula
$m=\frac{p_2-p_1}{x_2-x_2}=\frac{737.500-547.500}{50.000-10.000}=4.75$
$p-p_1=m(x-x_1)$
$C(x)-547.500=4.75(x-10.000)$
$C(x)=4.75x+500.000$
b) $C(x)=mx+b$
with $b$ is a fixed cost
So $b=500.000$
c) with $x=100.000$
$C(100.000)=4.75(100.000)+500.000=975.000$
d) $C(x)=mx+b$
with $m$ is the marginal cost
so The marginal cost is $4.75$