Question 1098380
Graphing the feasible region, two points are clear, the other two you need to solve for. 
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*[illustration DFC1.JPG].
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{{{7x-4(8)=14}}}
{{{7x-32=14}}}
{{{7x=46}}}
{{{x=46/7}}}
({{{46/7}}},{{{8}}})
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Next solve for the intersection of the two lines,
{{{7x-4y=14}}}
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{{{2x+y=10}}}
{{{8x+4y=40}}}
Adding to the first equation,
{{{7x-4y+8x+4y=14+40}}}
{{{15x=54}}}
{{{x=54/15}}}
So then,
{{{2(54/15)+y=150/15}}}
{{{108/15+y=150/15}}}
{{{y=42/15}}}
({{{54/15}}},{{{42/15}}})
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*[illustration DFC2.JPG].
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Now check the value of the function at each of the vertices. 
I'll do one, you do the other three the same way.
(2,6)
{{{z=4x+2y}}}
{{{z(2,6)=4(2)+2(6)=8+12=20}}}
Do the others exactly the same way.