Question 348454
{{{A+B=18}}}
THe product is,
{{{P=A*B}}}
SUbsitute from above,
{{{A=18-B}}}
{{{P=(18-B)B=18B-B^2}}}
To find the maximum, convert to vertex form, {{{y=a(x-h)^2+k}}}, since the maximum occures at the vertex (h,k).
Complete the square to convert to vertex form,
{{{P=-(B^2-18B)}}}
{{{P=-(B^2-18B+81)+81}}}
{{{P=-(B-9)^2+81}}}
The maximum occurs at B=9, when A=9, and P=81.