# Thread: [SOLVED] Poster Optimization Problem

1. ## [SOLVED] Poster Optimization Problem

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.

2. Originally Posted by biermann33
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

### the top and bottom margins of a poster are

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