Answer
a. $C(x)=100000+100x$
b. $\bar C(x)=100+\frac{100000}{x}$
c. $\bar C(500)=300$, $\bar C(1000)= 200$, $\bar C(2000)=150$, $\bar C(4000)125$
d. $\bar C=100$. See explanations.
Work Step by Step
a. Based on the given conditions, we have
$C(x)=100000+100x$
b. The average cost is given by
$\bar C(x)=\frac{100000+100x}{x}=100+\frac{100000}{x}$
c. (i) Using the given values, we have
$\bar C(500)=100+\frac{100000}{500}=100+200=300$ dollars
(the average cost to produce 500 bikes is 300 dollars).
(ii) Similarly, we have
$\bar C(1000)=100+\frac{100000}{1000}=100+100=200$ dollars
(the average cost to produce 1000 bikes is 200 dollars).
(iii) $\bar C(2000)=100+\frac{100000}{2000}=100+50=150$ dollars
(the average cost to produce 2000 bikes is 150 dollars).
(iv) $\bar C(4000)=100+\frac{100000}{4000}=100+25=125$ dollars
(the average cost to produce 4000 bikes is 125 dollars).
d. The horizontal asymptote can be found by letting $x\to\infty$, which gives $\bar C=100$. This means that when the number of bikes produced is extremely large, the average cost will be close to 100 dollars.
