Question 966510
First map the feasible region.
 *[illustration FEAS.JPG].
Find the point of intersection.
{{{4x+7y=28}}}
{{{10x-7y=28}}}
Add the equations together,
{{{14x=56}}}
{{{x=4}}}
Then,
{{{16+7y=28}}}
{{{7y=12}}}
{{{y=12/7}}}
Now from the graph, you have all the vertices of the feasible region.
({{{0}}},{{{0}}})
({{{0}}},{{{4}}})
({{{14/5}}},{{{0}}})
({{{4}}},{{{12/7}}})
The extrema of the function occur at these vertices. 
({{{0}}},{{{0}}}) : {{{z=3(0)+5(0)=0}}}
({{{0}}},{{{4}}}): {{{z=3(0)+5(4)=20}}}
({{{14/5}}},{{{0}}}): {{{z=3(14/5)+5(0)=42/5=8.4}}}
({{{4}}},{{{12/7}}}): {{{z=3(4)+5(12/7)=12+60/7=84/7+60/7=144/7=20&4/7}}}