Answer
a. $C(x)=100000+100x$
b. $C(x)=\frac{100000+100x}{x}$
c. $C(500)=100000+100\times500=150000$,
$C(1000)=100000+100\times1000=200000$,
$C(2000)=100000+100\times2000=300000$,
$C(4000)=100000+100\times4000=500000$
d. $y=100$
Work Step by Step
a. Monthly cost function as a function of $x$ items is monthly fixed cost plus the cost of producing $x$ items.
Therefore, $C(x)=100000+100x$,
b. The average cost function is the monthly cost function divided by the number of items produced, in this case $x$.
Therefore, $C(x)=\frac{100000+100x}{x}$.
c. $C(500)=100000+100\times500=150000$,
$C(1000)=100000+100\times1000=200000$,
$C(2000)=100000+100\times2000=300000$,
$C(4000)=100000+100\times4000=500000$
$C(500)$ is the cost of producing $500$ bikes and so on.
d. The rules of horizontal asymptote of a rational function are as follows,
1. If the numerator's degree is less than the denominator's degree, then the horizontal asymptote is $y = 0$.
2. If the numerator's degree is equal to the denominator's degree, then the horizontal asymptote is $y = c$, where $c$ is the ratio of the leading terms of the the numerator and the denominator.
3. If the numerator's degree is more than the denominator's degree, then there is no horizontal asymptote.
In the case of Average cost function $C(x)=\frac{100000+100x}{x}$, the degree of the numerator is equal to the degree of denominator.
Therefore,
$y=\frac{100}{1}=100$.
This horizontal asymptote in this case means that the more bicycle produced each each month, the closer the average cost per bicycle for the
company comes to $100$. ·The least possible cost per bicycle is approaching $100$.
