91Ó°ÊÓ

The linear cost function is $C\left(x\right)=mx+b$, where the y-intercept b represents the fixed costs of operating a business and the slope m represents the cost of each item produced.

A small bicycle manufacturer has daily fixed costs of $1800 and the manufacturing cost of each bicycle is $90.

Find a linear model that expresses the cost C of manufacturing x bicycles in a day.

A small bicycle manufacturer has daily fixed costs of $1800. so y-intercept is $b=1800$.

The manufacturing cost of each bicycle is $90. it will as per number of bicycle manufactured so this is slope $m=90$.

So the equation becomes $C\left(x\right)=90x+1800$.

The graph for cost function $C\left(x\right)=90x+1800$is as follows,

Find the cost of manufacturing 14 bicycles in a day.

We have $x=14$, find $C\left(x\right)$.

$$\begin{gathered} C\left(x\right)=90x+1800 \\ =90\left(14\right)+1800 \\ =3060 \end{gathered}$$

The cost of manufacturing 14 bicycles in a day is $3060.

Find how many bicycles could be manufactured for $3780.

We have $C\left(x\right)=3780$. find x.

$$\begin{gathered} C\left(x\right)=90x+1800 \\ 3780=90x+1800 \\ 1980=90x \\ 22=x \end{gathered}$$

22 bicycles could be manufactured for $3780.