Answer
$26.552$ hundred thousand space heaters
Work Step by Step
Given \begin{equation}
C(h)=2.29 \sqrt{h}+3.2.
\end{equation} First solve for $h$ in term of $C$.
\begin{equation}
\begin{aligned}
2.29 \sqrt{h}+3.2&=C\\
\sqrt{h}&=\frac{C-3.2}{2.29 } \\
\left(\sqrt{h}\right)^2& =\left( \frac{C-3.2}{2.29 } \right)^2\\
h& = \left( \frac{C-3.2}{2.29 } \right)^2.
\end{aligned}
\end{equation} Now, set $C = 15$ to find the number of heaters that must be produced.
\begin{equation}
\begin{aligned}
h&=\left( \frac{15-3.2}{2.29 } \right)^2\\
&=26.552.
\end{aligned}
\end{equation} The company can make about $26.552$ hundred thousand space heaters with a budget of $\$15$ million.
