You are designing a rectangular poster to contain 50 in2 of printing with a 4-in margin at the top and bottom and a 2-in margin at each side.
what overall dimensions will minimize the amount of paper used?

W = 7.53 inches

H = 30.14 inches

Explanation:

Printing area is:

Solving for :

The total area of the paper is:

  Replacing :

If we derivate and equal zero to find the minimum:

  So,

The final dimensions of the paper are:

W = 3.53 + 4=7.53-inch

H = 14.14 + 16= 30.14-inch

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explanation:

a and b sometimes have a positive value