The top and bottom margins of a poster are 6 cm and the side margins are each 7 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.

Answer 1

let length of printed area be x
let the width be y

so xy = 384
y = 384/x

length of paper = x+12
width of paper = y+14

area of paper = (x+12)(y+14)
= xy + 14x + 12y + 168
= x(384/x) + 14x + 14(384/x) + 168
= 384 + 14x + 5376/x + 168

d(area)/dx = 14 - 5376/x^2
= 0 for min of area

5376/x^2 = 14
14x^2 = 5376
x^2 = 384
x = √384 = appr 19.596 cm
then y = 19.596

poster is 19.596+12 by 19.596+14
etc

Answer 2

Wrong answer