# A poster is to contain 50cm2 of matter with borders of 4 cm at top and bottom and of 2 cm on each side. Find the dimensions if the total area of the poster is minimum.

Jitender Singh IIT Delhi
8 years ago
Ans:
Let the length & width of the matter area of poster to be ‘l’ & ‘b’
Given:
$lb = 50 cm^{2}$
Area of poster:
$A = (l+8)(b+4)$
$A = 82 + 4l + 8b$
$A = 82 + 4l + \frac{400}{l}$
$\frac{\partial A}{\partial l} = 4 - \frac{400}{l^{2}} = 0$
$l = 25$
$\Rightarrow b= 2$
Dimensions:
Length = l + 8 = 33 cm
Width = b + 4 = 6 cm
Thanks & Regards
Jitender Singh
IIT Delhi