Question

if we have that x+2y=40
then the largest possible value for xy is what?
maximum product = ?

Answer 1

you remeber that fence problem? this can be done in the similar fashion.

Answer 2

differenciate x+27=40 wrt x. You have 1+2dy/dx=0
that is dy/dx=-1/2

Now the max. product P=xy is constant so, differenciating that
0=x(dy/dx)+y
that is, x(-1/2)+y=0
that is 2y=x

Answer 3

btw, it's not x+27, it's x+2y (pardon that typo)

Answer 4

Thus, y is 40/3 and x is 80/3
the product is 3200/9