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The given function is $C\left(x\right)=20x+6000$represents the cost to produce $x$, number of items.

We have to find 鈸� the average cost function, $c\left(x\right)$鈸� how many items should be produced so that the average cost is less than $\$60$?

The average cost function is $c\left(x\right)=\frac{C\left(x\right)}{x}$

The average cost function is$C\left(x\right)=\frac{20x+6000}{x}$

Substitute the rational expression for $c\left(x\right)$.

role="math" localid="1645121918700" $\frac{20x+6000}{x}<60$$x鈮�0$

Subtract $60$to get 0 on the right.

$$\begin{gathered} \frac{20x+6000}{x}-60<60-60 \\ \frac{20x+6000}{x}-60<0 \end{gathered}$$

$\frac{20x+6000}{x}-60路\frac{x}{x}<0$

$$\begin{gathered} \frac{20x+6000}{x}-\frac{60x}{x}<0 \\ \frac{20x-60x+6000}{x}<0 \end{gathered}$$

role="math" localid="1645122254243" $\frac{-40x+6000}{x}<0$

Factor the numerator to show all factors.

$\frac{-40(x-150)}{x}<0$

$$\begin{gathered} -40(x-150)=0x=0 \\ -40鈮�0x-150=0 \\ x=150 \end{gathered}$$

More than $150$items must be produced to keep the average cost below $\$60$per item.