  A rectangular page will contain 50 square inches of print. The margins at the top andbottom of the page are 2 inches wide. The margins on each side are 1 inch wide. Find thedimensions of the page that will minimize the amount of paper used.

Question

A rectangular page will contain 50 square inches of print. The margins at the top and
bottom of the page are 2 inches wide. The margins on each side are 1 inch wide. Find the
dimensions of the page that will minimize the amount of paper used.

Step 1

Let us consider the paper size of length x inches and width to be y inches.

As the margin at the top and bottom of the page are 2 inches wide the length of the printed space would be x-4 inches and the margins on each side are 1 inch wide the width would be y-2 inches.

As the printed area being 50 it means that:

Step 2

As the area of a rectangle is given as: length x width

Therefore, area would be given as:

Step 3

To minimize the paper size, we need to differentiate the function a...

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Calculus 