Answer
a. $110$ dollars.
b. $80$ dollars.
c. $79.9\approx80$ dollars.
Work Step by Step
a. Given the cost equation $c(x)=2000+100x-0.1x^2$, we can obtain the cost for producing the first 100 washing machines is $c(100)=2000+100(100)-0.1(100)^2=11000$
Thus the average cost per machine is $\bar c=11000/100=110$ dollars.
b. The marginal cost when 100 washing machines are produced is the value of the derivative of the cost function at that point. We have $c'(x)=100-0.2x$ and $c'(100)=100-0.2(100)=80$ dollars.
c. Let $x=101$; we have $c(101)=2000+100(101-0.1(101)^2=11079.9$ dollars. Thus the cost of producing one more washing machine after the first 100 have been made is:
$c(101)-c(100)=11079.9-11000=79.9\approx80$ dollars
and this is the marginal cost.
