Question 346507
Determine the vertices.
{{{x=30}}},{{{y=40}}}
(30,40)
{{{x=60}}},{{{y=40}}}
(60,40)
{{{x+y=120}}}
{{{30+y=120}}}
{{{y=90}}}
(30,90)
{{{x+y=120}}}
{{{60+y=120}}}
{{{y=60}}}
(60,60)
.
.
{{{drawing(300,300,-10,90,-5,95,
grid(1),
blue(line(30,-100,30,200)),
blue(line(60,-100,60,200)),
green(line(-100,100,200,100)),
green(line(-100,40,200,40)),
circle(30,40,1.8),

circle(60,40,1.8),
circle(60,60,1.8),
circle(30,90,1.8),
graph(300,300,-10,90,-5,95,120-x))}}}
.
.
The maximum (and minimum) values occur(s) at the vertices.
(30,40):{{{P= 150x + 65y=150(30)+65(40)=7100}}}
(60,40):{{{P= 150x + 65y=150(60)+65(40)=11600}}}
(30,90):{{{P= 150x + 65y=150(30)+65(90)=10350}}}
(60,60):{{{highlight(P= 150x + 65y=150(60)+65(60)=12900)}}}
Make 60 of each to maximize profits.