MHB How Can I Maximize the Area of a Window Using These Equations?

[markosheehan]

View attachment 5907

Does anyone know how to work this out. Any help much appreciated. it is question 32 I'm stuck on

 

[Greg]

Two equations are relevant here:

$$A=\dfrac12\pi r^2+2rh\quad(1)$$

and

$$P=2h+2r+\pi r=2h+(2+\pi)r=12+3\pi\quad(2)$$

Now proceed as follows:

a) solve $(2)$ for $h$ in terms of $r$ and substitute that for $h$ in $(1)$, giving $(1*)$.

b) differentiate $(1*)$ with respect to $r$, equate the result to $0$ and solve for $r$.

c) state $2r$ in meters as the width of the window with maximum area.