Question

Write a cost function for the problem. Assume that the relationship is linear. Fixed cost, $410; 5 items cost $5,590 to produce. A. C(x)-1.036x + 410 ? B. C(x)= 1,036x +5,590 ? ?. ?(x) 2,072x +5,590 O D. C(x)-2,072x+410

Answer 1

Answer:

The required cost function is $C(x)=1036x+410$.

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

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

The equation of cost function is

$y-410=\frac{5590-410}{5-0}(x-0)$

$y-410=\frac{5180}{5}(x)$

$y-410=36x$

$y-410=1036x$

Add 410 on both the sides.

$y=1036x+410$

The required cost function is

$C(x)=1036x+410$

Therefore the required cost function is $C(x)=1036x+410$.