ok, so we want the precalc way of doing this. that's fine.

so we have

..........(1)

and

................(2)

we want to maximize P. to do this, it would be much simpler to work with one variable. so solve for one variable in terms of the other using our constraint.

From equation (1),

, so plug that into P

this is a downward opening parabola, it's maximum value occurs at the vertex. we can find the vertex by completing the square, but that is too much work. use the vertex formula:

**Vertex formula: **for a parabola

, the x value for the vertex is given by:

, and thus the vertex is given by

so here, the vertex occurs when

so

but we have

there are your two numbers

now, can you state the maximum product?