The number of luxury home sales S(t) in a major Canadian urban area over a period of 12 year is given by:

\(\displaystyle\Rightarrow{S}{\left({t}\right)}={5.8}{t}^{2}-{81.2}{t}+{1200}\)

For minimum number of sales:

\(\displaystyle\Rightarrow\frac{{{d}{S}{\left({t}\right)}}}{{\left.{d}{t}\right.}}={0}\)

\(\displaystyle\Rightarrow\frac{{{d}{\left({5.8}{t}^{2}-{81.2}{t}+{1200}\right)}}}{{\left.{d}{t}\right.}}={0}\)

\(\displaystyle\Rightarrow{11.6}{t}-{81.2}={0}\)

\(\displaystyle\Rightarrow{11.6}{t}={81.2}\)

\(\displaystyle\Rightarrow{t}=\frac{{{81.2}}}{{{11.6}}}\)

\(\displaystyle\Rightarrow{t}={7}\)

So, minimum number of sales is given by

\(\displaystyle\Rightarrow{S}{\left({7}\right)}={5.8}{\left({7}\right)}^{2}-{81.2}{\left({7}\right)}+{1200}\)

\(\displaystyle\Rightarrow{S}{\left({7}\right)}={284.2}-{568.2}+{1200}\)

\(\displaystyle\Rightarrow{S}{\left({7}\right)}{915.8}\)

\(\displaystyle\Rightarrow{S}{\left({7}\right)}\stackrel{\sim}{=}{916}\)