Optimization - window with arch
Calculus optimization scenario involving a window shaped like a semicircular arch atop a rectangle.
For a given perimeter of this window, use calculus to find the dimensions (diameter of semicircle x, height of rectangle y) that would maximize the window area. Use this construction to verify your answer and visualize the geometry. Drag the large point in the left graphics view to adjust the size of the window. For keyboard control, select the point and use the arrow keys to adjust, also pressing shift key for finer control.
"Lengths" toggle displays length values to three decimal places in the left graphics view.
"Area" toggle graphs area as a function of x in the right graphics view.
"Window type" button toggles between three window designs, including all displayed segments in the calculation of perimeter:
- outer edges only (Use this if you're my student checking a homework exercise, even though textbook graphic shows a horizontal interior crossbar)
- outer edges plus one horizontal interior crossbar
- outer edges plus two horizontal one one vertical interior crossbars