Indian Institute of Foreign Trade 2008 Solved Paper

Z is the number of items produced by the company.
Total cost, $\mathit{R}=\frac{1}{10}\left({\mathit{Z}}^3-5{\mathit{Z}}^2+10\mathit{Z}+5\right)$
As we can see, the term '5' does not vary with the number of quantities produced. Therefore, 5 is the fixed cost.
Variable cost $=\frac{1}{10}\left({\mathit{Z}}^3-5{\mathit{Z}}^2+10\mathit{Z}\right)$
Average variable cost = Total variable cost/ number of quantities.
Average variable cost $=\frac{1}{10}\left({\mathit{Z}}^2-5\mathit{Z}+10\right)$
$=\frac{{\mathit{Z}}^2-50\mathit{Z}+100}{10}$
$=\frac{\left({\mathit{Z}}^2-50\mathit{Z}+625\right)-525}{10}$
$=\frac{{\left(\mathit{Z}-25\right)}^2-525}{10}$
As we can see, the least value of the expression will be obtained at $\mathit{Z}=25$
Therefore, option C is the right answer.