Answer
a. $C(x)=\frac{300000+10x}{x}$
b. $y=10$
Work Step by Step
The monthly cost function is monthly fixed cost plus the cost of producing $x$ items produced monthly.
$C(x)=300000+10x$ is the cost function of producing $x$ items in a month.
a. the average cost function is the cost function divided by the number of items produced which is $x$.
$C(x)=\frac{300000+10x}{x}$
b. The rules of horizontal asymptotes are as follows:
1. If the numerator's degree is less than the denominator's degree, there is a horizontal asymptote at y = 0.
2. If the numerator's degree equals the denominator's degree, there is a horizontal asymptote at y = c, where c is the ratio of the leading terms or their coefficients.
3. If the numerator's degree is more than the denominator's degree, then there is no horizontal asymptote.
In this case, the degree of numerator is equal to the degree of the denominator. Therefore, the Horizontal asymptote are,
$y=\frac{10}{}=10$
The horizontal asymptote represents in this case, the more radio player produced in a month, the closer the average cost per player comes to $10$. The least possible cost per player is approaching $10$.
