Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Optimization semicircle problem

  1. Apr 8, 2008 #1
    [SOLVED] Optimization problem

    1. The problem statement, all variables and given/known data

    A Norman window has the shape of a semicircle atop a rectangle so that the diameter of the smicircle is equal to the width of the rectangle. What is the area of the largest possible Norman window with a perimeter of 28 feet?

    2. Relevant equations


    After solving for b and plugging b into the Area formula I cannot determine the local max. Is the algebra or derivative wrong?

    3. The attempt at a solution please see attachment
     

    Attached Files:

  2. jcsd
  3. Apr 8, 2008 #2
    Thanks for your suggestion, the perimeter of a circle is also also pi*diameter, so then a semi-circle P=1/2pi*d. Which is what I have for the 1st equation
     
  4. Apr 9, 2008 #3
    Solution:
    A(x)=14b-(4+pi/8)*b^2
    A'(x)=14-(4+pi/4)*b
    Solve for b: (56/4+pi)
    Insert b into the original area formula A(x) and the area of the largest possible window=54.8897ft
    The problem was set up correctly except that I rounded off to only one significant figure and that's why my original answer didn't match the answer provided in the book.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook