Select the correct answer.

The total daily cost (in dollars) of manufacturing scented candles is given by the function [tex]C(b)=250+3b[/tex], where [tex]b[/tex] is the number of candles manufactured. Which function represents the average manufacturing cost, [tex]A[/tex], in terms of [tex]b[/tex]?

A. [tex]A(b)=\frac{b}{250+3b}[/tex]
B. [tex]A(b)=\frac{250+3b}{b}[/tex]
C. [tex]A(b)=(250+3b) \times b[/tex]
D. [tex]A(b)=250+4b[/tex]



Answer :

To determine which function represents the average manufacturing cost [tex]\(A(b)\)[/tex] in terms of the number of cars manufactured [tex]\(b\)[/tex], we need to understand the relationship between the total cost and the average cost.

The total daily cost of manufacturing [tex]\(b\)[/tex] scented candles is given by the function:
[tex]\[ C(b) = 250 + 3b \][/tex]

The average manufacturing cost [tex]\(A(b)\)[/tex] is defined as the total cost divided by the number of units [tex]\(b\)[/tex]. Mathematically, this is expressed as:
[tex]\[ A(b) = \frac{C(b)}{b} \][/tex]

Plugging the given total cost function into this formula, we get:
[tex]\[ A(b) = \frac{250 + 3b}{b} \][/tex]

Thus, the function that represents the average manufacturing cost [tex]\(A(b)\)[/tex] in terms of [tex]\(b\)[/tex] is:
[tex]\[ A(b) = \frac{250 + 3b}{b} \][/tex]

Among the provided options, the correct one is:
B. [tex]\( A(b) = \frac{250 + 3b}{b} \)[/tex]