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: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].