Answer
Maximum revenue occurs when $70$ houses are built.
The corresponding revenue is $R={\$} 9,800,000$.
Work Step by Step
The given data points are
$(p, q)=(40$, $200,000)$ and $(60,$ $160,000).$
The line passing through these points is obtained from
$y-y_{1}=\displaystyle \frac{y_{2}-y_{1}}{x_{2}-x_{1}}(x-x_{1})$
$y-200,000=\displaystyle \frac{-40,000}{20}(x-40)$
$y=-2000p+80,000+200,000$
$q=-2000p+280,000$.
Revenue is $R=pq=-2000p^{2}+280,000p$.
The graph of R is a parabola opening down. The maximum occurs at the vertex,
$-b/(2a)=$ $70$ houses
$R(70)=-2000(70)^{2}+280,000(70)={\$} 9,800,000$.
