2x+3y=60 solve for x...
x=(60-3y)/2
p=xy^3, using x from above:
p=y^3(60-3y)/2
p=(60y^3-3y^4)/2
dp/dy=(180y^2-12y^3)/2
dp/dy=90y^2-6y^2
dp/dy=0 when:
90y^2-6y^3=0
6y^2(15-y)=0, we know y>0 so
y=15, since x=(60-3y)/2
x=7.5
(We solved it this way because otherwise you get quartic equations and cubic derivatives, yuck :P)
Here you go :) I sent the work in the picture below
I took a picture on my calculator of what the graph should look like.
11-2x would be the answer u are looking for. Hope this helps!
