Question

A small bicycle manufacturer has daily fixed costs of $1913 and each bicycle costs $80 to manufacture. Let x represent the number of bicycles manufactured and C(x) represents the cost of manufacturing. (a) Write a linear function that models this situation.C(x)= _____(b) C(5)=____. This means that the cost of manufacturing ____ bicycles in a day is $_____(c) Find the value of x if C(x) = 2873. (Express this situation using function notation, and interpret it in the context of this problem.)X=____ when C(x)=2873. This means that the cost of manufacturing ____ bicycles in a day is $_____

Answer 1

`\begin{gathered} a)\text{ C\lparen x\rparen=80x+1913} \\ b)\text{ C\lparen5\rparen=2,313. This means that the cost of manufacturing 5 bicycles in a day is \$2,313} \\ c)\text{ x=12 when C\lparen x\rparen=2873.} \\ \text{ This means that the cost of manufacturing 12 bicycles in a day is \$2,873} \end{gathered}`

Explanation:

The situation is represented by a linear function since has an initial value or cost and it increases at a constant rate of change. Therefore, by the definition of a linear function:

`\begin{gathered} y=mx+b \\ where, \\ m=\text{ slope} \\ b=\text{ y-intercept} \end{gathered}`

Therefore, if the daily fixed cost is $1913 and each bicycle costs $80 to manufacture:

a)

`C(x)=80x+1913`

If x represents the number of bicycles manufactured, C(5) represents the cost of 5 bicycles manufactured in a day:

b)

`\begin{gathered} C(5)=80(5)+1913 \\ C(5)=\text{ \$2,313} \end{gathered}`

c) Find the value of x, substitute C(x)=2873

`\begin{gathered} 2873=80x+1913 \\ 80x=2873-1913 \\ x=(960)/(80) \\ x=12 \\ \text{ This means that the cost of manufacturing 12 bicycles in a day is \$2,873} \end{gathered}`