Find the width , in cm, of the poster with the SMALLEST total area.

Question

The top and bottom margins of a poster are each 5 cm, and the side margins are each 3 cm. The area of the printed material on the poster is fixed at 85 cm²

Answer 1

A= (x+10)(y+6) =xy+10y+6x+60

xy= 85

y=85/x

A=6x+10y+145

=6x+850/x+145

A' = 6 -850/x^2 =0

6x^2=850

x^2=425/3

x=5sqr17/sqr3=11.9

y=85/11.9=7.14

x+10=17.9

y+6=13.14 cm. = width that minimizes area

A=(x+10)(y+6)=235.2 cm^2=min area

or

x=85/y

A=6(85)/y+10y+146

A=510/y +10y +146

A'=10-510/y^2=0

y^2=51

y=sqr51=7.14

y+6=13.14 cm= width