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5.2k views
in Applications of Differential Calculus by (48.7k points)
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A rectangular page is to contain 24 cm2 of print. The margins at the top and bottom of the page are 1.5 cm and the margins at other sides of the page is 1 cm.

What should be the dimensions of the page so that the area of the paper used is minimum.

1 Answer

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by (49.4k points)
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Best answer

Let the length of the printed page be = x cm and breadth = y cm 

Now xy = 24 

⇒ y = 24/x ... (1)

The length of the paper = y + 3 

Area A = (x + 2)(y + 3) 

= xy + 3x + 2y + 6 

= 24 + 3x + 2y + 6 

= 3x + 2y + 30 … (2) 

Substituting (1) in (2) we get

∴ Dimensions of the paper are 

x + 2 = 4 + 2 = 6 cm 

and y + 3 = 6 + 3 = 9 cm

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