Question 932521
Slope intercept form is {{{y=mx+b}}}
{{{3x+5y>=35}}}
{{{5y>=-3x+35}}}
{{{y>=-(3/5)x+7}}}
{{{graph(300,300,-2,10,-2,10,y>=-(3/5)x+7)}}}
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{{{2x+y<=14}}}
{{{y<=-2x+14}}}
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{{{graph(300,300,-2,10,-2,10,y<=-2x+14)}}}
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{{{drawing(300,300,-2,10,-2,10,grid(1),circle(0,0,0.3),circle(7,0,0.3),circle(0,7,0.3),circle(5,4,0.3),graph(300,300,-2,10,-2,10,-(3/5)x+7,-2x+14))}}}
The easy vertices are (0,0),(0,7),(7,0).
To find the remaining one, set the two linear equations equal to each other.
{{{-2x+14=-(3/5)x+7}}}
{{{-2x+(3/5)x=-7}}}
{{{-(10/5)x+(3/5)x=-7}}}
{{{-(7/5)x=-7}}}
{{{x=5}}}
Then,
{{{y=-2(5)+14}}}
{{{y=4}}}
(5,4) is the final vertex.
Now check the function at each point.
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(0,0):{{{P=3(0)+2(0)=0}}}<-- Min
(7,0):{{{P=3(7)+2(0)=21}}}
(0,7):{{{P=3(0)+2(7)=14}}}
(5,4):{{{P=3(5)+2(4)=23}}}<-- Max