Question 856331
Just as a note, <= is less than or equal and >= is greater t
{{{x+2y<=16}}}
{{{graph(300,300,-2,10,-2,10,y<=(16-x)/2)}}}
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{{{y-x<=5}}}
{{{graph(300,300,-2,10,-2,10,y<=x+5)}}}
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First graph the region.
{{{drawing(300,300,-2,10,-2,10,
green(line(-20,4,20,4)),
green(line(1,-20,1,20)),
graph(300,300,-2,10,-2,10,(16-x)/2,x+5))}}}
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Find the points of intersection.
(1,4)
(1,6)
(2,7)
(8,4)
First graph the region.
{{{drawing(300,300,-2,10,-2,10,
circle(1,4,0.2),
circle(1,6,0.2),
circle(2,7,0.2),
circle(8,4,0.2),
green(line(-20,4,20,4)),
green(line(1,-20,1,20)),
graph(300,300,-2,10,-2,10,(16-x)/2,x+5))}}}
The min and max values occur at one of these vertices.
{{{C=12x-4y=12(1)-4(4)=12-16=-4}}}
{{{C=12x-4y=12(1)-4(6)=12-24=-12}}}
{{{C=12x-4y=12(2)-4(7)=24-28=-4}}}
{{{C=12x-4y=12(8)-4(4)=96-16=80}}}