Since the function of the cost is
[tex]C(x)=4.1x+9500[/tex]Where x is the number of the items
a) There were 200 items
x = 200
[tex]\begin{gathered} C(x)=4.1(200)+9500 \\ C(x)=820+9500 \\ C(x)=10320 \end{gathered}[/tex]To find the average cost per item, find
[tex]\begin{gathered} \text{Ave. =}\frac{C(x)}{x} \\ \text{Ave. = }\frac{10320}{200} \\ \text{Ave. =51.6} \end{gathered}[/tex]b) There were 2000 items
[tex]x=2000[/tex][tex]\begin{gathered} C(2000)=4.1\times2000+9500 \\ C(2000)=17700 \end{gathered}[/tex]Find the average as the same above
[tex]\begin{gathered} \text{Ave. = }\frac{17700}{2000} \\ \text{Ave. = 8.85} \end{gathered}[/tex]c) There were 5000 items
[tex]x=5000[/tex][tex]\begin{gathered} C(5000)=4.1(5000)+9500 \\ C(5000)=30000 \end{gathered}[/tex]Divide it by 5000 to find the average
[tex]\begin{gathered} \text{Ave. = }\frac{30000}{5000} \\ \text{Ave. = 6} \end{gathered}[/tex]