Answer
a) $C=8000+22x$
b) $R=49x$
c) $27x-8000$
d) $297$
Work Step by Step
a) Let $x$ be the number of tires.
The total cost $C$ consists of the set up cost and the production cost for $x$ tires:
$$C=8000+22x.$$
b) The revenue $R$ for selling $x$ tires is the product between the number of sold tires and the sale price of each tire:
$$R=49x.$$
c) The profit $P$ is the difference between the revenue and the cost:
$$\begin{align*}
P&=R-C\\
&=49x-(8000+22x)\\
&=49x-8000-22x\\
&=27x-8000.
\end{align*}$$
d) In order to break even we must have the revenue equal to the cost, therefore the profit should be zero. We solve the equation for $x$:
$$\begin{align*}
P&=0\\
27x-8000&=0\\
27x&=8000\\
x&=\dfrac{8000}{27}\\
&\approx 297.
\end{align*}$$
So $297$ items should be sold.
