Question 1078551
{{{x}}}= width of the printed part, in inches
{{{y}}}= height of the printed part, in inches
{{{xy=24}}}= area of the printed part, in square inches
So, {{{y=24/x}}}
{{{x+2*1=x+2}}}= width of the page, in inches
{{{y+2*1.5=y+3}}}= height of the page, in inches
The area of the page (in square inches) is
{{{A=(x+2)(y+3)=xy+3x+2y+6=24+3x+2(24/x)+6=3x+48/x+30}}}
One way to d=find the minimum is
to calculate the derivative {{{dA/dx}}} ,
and solve the equation {{{dA/dx=0}}} .
{{{dA/dx =3-48/x^2=(3x^2-48)/x^2=3(x^2-16)/x=3x-4x+4/x2}}}
{{{dA/dx=0}}} ---> {{{x=4}}} ,
The width and height of the paper are
{{{x+2=4+2=6}}} and
{{{y+3=24/x+3=48/4+3=6+3=9}}} .
The dimensions of the page, so that the least amount of paper is used
must be 6 inches wide by 9 inches tall.