A small bicycle manufacturer has daily fixed costs of 1931 a

A small bicycle manufacturer has daily fixed costs of ?$1931 and each bicycle costs ?$79 to manufacture. Let x represent the number of bicycles manufactured and C(x) represents the cost of manufacturing. Complete parts ?(a) through ?(c).

fixed costs and each bicycle costs $79 to manufacture. Let x represent the number of bicycles manufactured a A small bicycle manufacturer has daily of $1931 C(x) represents the cost of manufacturing. Complete parts (a) through (c). (a) Write a linear function that models this situation. C(x) (b) Find C(6). Interpret your answer in the context of this problem C(6) This means that the cost of manufacturing bicycles in a day is (c) Find the value of xif C(x) 2800. Express this situation using function notation, and interpret it in the context of this problem. x when c(x) 2800. This means that the cost of manufacturing bicycles in a day is s

Solution

fixed cost of manufacturing the bicycles = $1931

variable cost of manufacturing one bicycle = $79

Let the number of bicycles manufactured =x

Total cost of manufacuring bicycles= C(x)

(a)C(x) can be expressed as

C(x) = 1931 + 79*x

(b) C(6)=?

We know, C(x) = 1931 + 79*x

C(6) = 1931 + 79*6

C(6)=474+1931

C(6)= 2405

This means that cost of manufacturing 6 bicycles ina day is $2405.

(c) C(x)=2800

We know C(x) = 1931 + 79*x

=> 79x=C(x)-1931

=> x= (C(x)-1931)/79

Now C(x)=2800

=> x=(2800-1931)/79

=>x=11

Therefore, x=11 when C(x)=2800.

This means that the cost of manufacturing 11 bicycles in a day is 2800 $.