poster dimensions

Question

The top and bottom margins of a poster are 6 cm and the side margins are each 2 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

A = (12+x)(4+y) xy=384 y=384/x

A = (12+x)(4+384/x) = 48 + 4x + 12(384)/x + (384)= 432 + 4x + 4608/x

A' = 4 -4608/x^2 = 0

4608/x^2 = 4

4x^2 = 4608

x^2 = 1152

x = sqr1152 = about 33.94

y = 384/33.94 = 11.31

dimensions of the poster that minimize area = 45.94 cm by 15.31 cm

min area = 703.34. the border has area = 2(6)(15.31) = 183.72 + 2(2)33.94 = 183.72 + 132.4 = 316.12

384 + 316.12 = 700.12 dimensions are slightly larger than 45.94 cm by 15.31