The cost per ton, [tex]\( y \)[/tex], to build an oil tanker of [tex]\( x \)[/tex] thousand deadweight tons was approximated by

[tex]\[ \bar{C}(x) = \frac{225,000}{x + 480} \][/tex]

for [tex]\( x \ \textgreater \ 0 \)[/tex]. Answer parts a through d.

a. Find [tex]\( \overline{C}(25) \)[/tex], [tex]\( \overline{C}(50) \)[/tex], [tex]\( \overline{C}(100) \)[/tex], [tex]\( \overline{C}(200) \)[/tex], [tex]\( \overline{C}(300) \)[/tex], and [tex]\( \overline{C}(400) \)[/tex].

[tex]\[
\begin{array}{rlr}
\overline{C}(25) & = 454.55 & \overline{C}(50) = 432.69 \\
\overline{C}(100) & = 394.74 & \overline{C}(200) = 335.82 \\
\overline{C}(300) & = 292.21 & \overline{C}(400) = 258.62
\end{array}
\][/tex]

(Type an integer or decimal rounded to one decimal place as needed.)



Answer :

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]