13 Nov 2021
Problem 23
Page 306
Section 4.6: Optimization Problems
Chapter 4: Applications of Differentiation
Textbook ExpertVerified Tutor
13 Nov 2021
Given information
A window which is shape of a rectangle surmounted by a semicircle so that the greatest possible amount of light admitted if the perimeter of the window is .
Step-by-step explanation
Step 1.
Let denote half the width of the rectangle (so is the radius of the semicircle), and let denote the height of the rectangle. Then the perimeter of the window is
Since the perimeter is , we have that
Therefore, the area of the window (which is proportional to the amount of light admitted), is given by
Substituting the above value for yields