Solution:
According to the solution of exercise 15, we have
Maximize 
, subject to the constraints
(i)
(ii)
Let’s construct a constrain table for the above
Table for (i)
![\[\begin{tabular}{|l|l|l|} \hline $\mathrm{x}$ & 0 & 60 \\ \hline $\mathrm{y}$ & 40 & 0 \\ \hline \end{tabular}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-0faab87b263774e69a5a863c8ea62938_l3.png "Rendered by QuickLaTeX.com")
Table for (ii)
![\[\begin{tabular}{|l|l|l|} \hline $\mathrm{x}$ & 0 & 50 \\ \hline $\mathrm{y}$ & 80 & 0 \\ \hline \end{tabular}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-dfdff2a60382231fea13d376660f1355_l3.png "Rendered by QuickLaTeX.com")
Next, solving (i) and (iii) we obtain
and 
It can be seen that the feasible region whose corner points are 
and 
.
Let’s evaluate the value of 
![\[\begin{tabular}{|l|l|} \hline Corner points & Value of $Z=x+y$ \\ \hline$O(0,0)$ & $Z=0+0=0$ \\ \hline$A(50,0)$ & $Z=50+0=50$ \\ \hline$B(300 / 7,80 / 7)$ & $Z=300 / 7+80 / 7=380 / 7=54.3$ \\ \hline$C(0,40)$ & $Z=0-40=40$ \\ \hline \end{tabular}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-403a31d10e104c3c131d8b4af50ced6b_l3.png "Rendered by QuickLaTeX.com")
From above table the maximum value of is 
So, the maximum distance that the man can travel is 
at 
.