Respuesta :
Answer:
The required cost function is [tex]C(x)=1036x+410[/tex].
Step-by-step explanation:
It is given that the cost function represents a linear relationship.
The fixed cost is $410 and the cost of 5 items is $5,590. It means the linear function passes through the points (0,410) and (5,5590).
If a line passes through two points then the equation of line is
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
The equation of cost function is
[tex]y-410=\frac{5590-410}{5-0}(x-0)[/tex]
[tex]y-410=\frac{5180}{5}(x)[/tex]
[tex]y-410=36x[/tex]
[tex]y-410=1036x[/tex]
Add 410 on both the sides.
[tex]y=1036x+410[/tex]
The required cost function is
[tex]C(x)=1036x+410[/tex]
Therefore the required cost function is [tex]C(x)=1036x+410[/tex].
The required cost function is [tex]\rm C(x)= 1,036x +410[/tex].
Given
The relationship is linear.
Fixed cost, $410; 5 items cost $5,590 to produce.
What is a linear equation?
An equation between two variables that gives a straight line when plotted on a graph.
The standard form represents the linear equation;
[tex]\rm y=mx+c[/tex]
The fixed cost is $410 and the cost of the 5 items is $5,590. It means the linear function passes through the points (0,410) and (5,5590).
If a line passes through two points then the equation of a line is;
[tex]\rm y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)\\\\y-410=\dfrac{5590-410}5-0}(x-0)\\\\y-410=\dfrac{5180}{5}x\\\\y-410=1036x\\\\y=1036x+410\\\\C(x)=1036x+410[/tex]
Hence, the required cost function is [tex]\rm C(x)= 1,036x +410[/tex].
To know more about the Linear equations click the link given below.
https://brainly.com/question/13275994
