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 386 square centimeters, find the dimensions of the poster with the smallest area.

Answer 1

If the printed area has width x and height y,
xy = 386

The total area is thus
a = (x+8)(y+4) = (x+8)(386/x + 4)
= 4x + 418 + 3088/x

max area is where da/dx=0

da/dx = 4 - 3088/x^2
so, da/dx = 0 when x = 2√193

Now just evaluate y.