Solution:
According to the solution of exercise 12, we have
The objective function for minimum cost is 
Subject to the constrains;
(i)
(ii)
(iii)
and 
(non-negative constraints)
Now, let’s construct a constrain table for the above Table for (i)
![\[\begin{tabular}{|l|l|l|} \hline x & 0 & 6 \\ \hline y & 15 & 0 \\ \hline Table for (ii) \\ \hline x & 0 & $7.5$ \\ \hline y & 15 & 0 \\ \hline Table & for (iii) \\ \hline x & 1 & 0 \\ \hline y & 1 & 0 \\ \hline \end{tabular}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-31b084eb60778619e6233860d2aab3e5_l3.png "Rendered by QuickLaTeX.com")
Next, solving (i) and (iii), we obtain
and 
, so the corner point is A 
On solving (ii) and (iii), we obtain
and 
, so the corner point is 
Here, 
is the shaded feasible region whose corner points are 
and 
On evaluating the value of 
, we get
![\[\begin{tabular}{|l|l|} \hline Corner point & Value of $\mathrm{Z}=400 \mathrm{x}+200 \mathrm{y}$ \\ \hline $\mathrm{A}(30 / 7,30 / 7)$ & $\mathrm{Z}=400(30 / 7)+200(30 / 7)=18000 / 7=2571.4$ \\ \hline $\mathrm{B}(5,5)$ & $\mathrm{Z}=400(5)+200(5)=3000$ \\ \hline $\mathrm{C}(0,15)$ & $\mathrm{Z}=400(0)+200(15)=3000$ \\ \hline \end{tabular}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-863e75548c6ce2c7ea85b74d18f79c83_l3.png "Rendered by QuickLaTeX.com")
It is seen from the table that the minimum value is 
So, the required minimum cost is Rs at