The top and bottom margins of a poster are 2 cm and the side margins are each 4 cm. If the area of printed material on the poster is fixed at 384 square centimeters, find the dimensions of the poster with the smallest area.
The top and bottom margins of a poster are 2 cm and the side margins are each 4 cm. If the area of printed material on the poster is fixed at 384 square centimeters, find the dimensions of the poster with the smallest area.
let $\displaystyle x$ = printed area width
$\displaystyle y$ = printed area length
$\displaystyle xy = 384$
$\displaystyle x = \frac{384}{y}$
poster width = $\displaystyle x+8$
poster length = $\displaystyle y+4$
$\displaystyle A = (x+8)(y+4)$
$\displaystyle A = \left(\frac{384}{y} + 8\right)(y+4)$
find $\displaystyle \frac{dA}{dy}$ and optimize