To find the cost per ton, [tex]\( \overline{C}(x) \)[/tex], for various values of [tex]\( x \)[/tex], we use the given formula:
[tex]\[ \overline{C}(x) = \frac{225,000}{x + 480} \][/tex]
Let's calculate [tex]\( \overline{C}(x) \)[/tex] for the given values of [tex]\( x \)[/tex]:
1. For [tex]\( x = 25 \)[/tex]:
[tex]\[
\overline{C}(25) = \frac{225,000}{25 + 480} = \frac{225,000}{505} \approx 445.5
\][/tex]
2. For [tex]\( x = 50 \)[/tex]:
[tex]\[
\overline{C}(50) = \frac{225,000}{50 + 480} = \frac{225,000}{530} \approx 424.5
\][/tex]
3. For [tex]\( x = 100 \)[/tex]:
[tex]\[
\overline{C}(100) = \frac{225,000}{100 + 480} = \frac{225,000}{580} \approx 387.9
\][/tex]
4. For [tex]\( x = 200 \)[/tex]:
[tex]\[
\overline{C}(200) = \frac{225,000}{200 + 480} = \frac{225,000}{680} \approx 330.9
\][/tex]
5. For [tex]\( x = 300 \)[/tex]:
[tex]\[
\overline{C}(300) = \frac{225,000}{300 + 480} = \frac{225,000}{780} \approx 288.5
\][/tex]
6. For [tex]\( x = 400 \)[/tex]:
[tex]\[
\overline{C}(400) = \frac{225,000}{400 + 480} = \frac{225,000}{880} \approx 255.7
\][/tex]
So, the rounded costs per ton, to one decimal place, are:
[tex]\[
\begin{array}{rlr}
\overline{C}(25) & = 445.5 & \overline{C}(50) = 424.5 \\
\overline{C}(100) & = 387.9 & \overline{C}(200) = 330.9 \\
\overline{C}(300) & = 288.5 & \overline{C}(400) = 255.7
\end{array}
\][/tex]
