The production manager of a company plans to include 180 sq. cm of actual
printed matter in each page of a book under production. Each page should have 2.5 cm
wide margin along the top and bottom and 2.0 cm wide margin along the sides. What
are the most economical dimensions of each printed page?
Let the width dimension of total page in cm, let the length dimension of total page in cm.
Given cm2.
The total area of the page will be
Substitute
Differentiate with respect to
Find the critical number(s)
We consider
If decreases.
If increases.
The function has a local minimum at
Since the function has the only extremum for then the function has the absolute minimum for at
Then
The most economical dimensions of each printed page are
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