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

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

Grade:Upto college level

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
9 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
askIITians Faculty

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