The top and bottom margins of a poster are 8 cm and the side margins are each 9 cm. If the area of printed material on the poster is fixed at 382 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=382
The area of the poster is
a = (x+18)(y+16)
= (x+18)(382/x + 16)
= 16x + 670 + 6876/x

For minimum area, da/dx=0, so

16 - 6876/x^2 = 0
x = 3/2 √191

Now you can figure the poster dimensions.