Optimization Problems

Question

The top and bottom margins of a poster are each 3 cm and the side margins are each 2 cm. If the area of printed material on the poster is fixed at 96 cm², find the dimensions of the poster with the smallest area.

width:

height:

Answer 1

margins at bottom and top are 3 cm

margins on sides are 2 cm

printed material inside the poster = 96 cm^2

what are the poster's dimensions that have the minimum area for the poster?

just an educated guess, but probably 12+3(2)=18 by 8+2(2) = 12 cm = 216 cm^2= min area

ratio 3/2 = 12/8 and 12x8=96

or set up a calculus problem

A=(6+x)(4+(96/x)=24+4x+576/x+ 96

A'= 4-576/x^2=0

4x^2=576

x^2=576/4=144

x=sqr144=12

dimentions are 12+6 by 96/12+4 = 18 by12