GPT答：

7i24.cn

To let in the most light, we want to maximize the area of the window. Let's call the radius of the semicircle "r" and the height of the rectangle "h". 

The perimeter of this window is made up of two straight sides (of length h) and half a circle (of circumference πr). So we can write an equation for 14 meters of framing materials: 

2h + πr/2 = 14 

Solving for h, we get: 

h = (14 - πr/2)/2 

Now we can write an equation for the area A in terms of r: 

A = πr^2/2 + hr 

Substituting our expression for h: 

A = πr^2/2 + r(14 - πr/2)/4  

Expanding and simplifying: 
A = (π/8)r^2 + 7r/2 - (π/8)r^3

To find where this function has a maximum, we take its derivative with respect to r and set it equal to zero:

dA/dr = (π/4)r - (3π/8)r^2 + 7/2
0 = dA/dr when r ≈ 1.82 or r ≈ 5.12

We can check that these are indeed maxima by looking at whether d²A/dr² is positive or negative at those points. When r ≈ 1.82, d²A/dr² > 0 so it's a local minimum; when r ≈ 5.12, d²A/dr² <0 so it's a local maximum.

Therefore, to let in the most light while using only 14 meters of framing materials per window, we should make each window with dimensions approximately:

- Height: h ≈ [(14 - π(5.12)/2)/4] ≈ 1.54 m
- Radius: r ≈ 5.12 m